ValProcessor.scala

trait Processor {
  def process(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit
}

class BMValsProcessor extends Processor {
  def process(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit = {
    println("in BMValsProcessor") ///actual business logic
  }
}

class BMValsProcessor2 extends Processor {
  def process(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit = {
    println("in BMValsProcessor2") ///actual business logic
  }
}

object ValProcessor {
  def main(args: Array[String]): Unit = {

    val df: DataFrameReader = null; // initialization of DataFrameReader
    val spark: SparkSession = null; // initialization of SparkSession

    val procs: Map[String, (DataFrameReader, SparkSession) => Unit] = getAllDefinedProcessors()

    procs.values.foreach(
      proc => proc(df, spark)
    )
  }

  def getAllDefinedProcessors(): Map[String, (DataFrameReader, SparkSession) => Unit] = {

    Map(
      "bm_vals" -> new BMValsProcessor().process,
      "bm_vals2" -> new BMValsProcessor2().process
    )
  }

}

1. new BMValsProcessor().process is link to function. Function takes (DataFrameReader, SparkSession) and returns Unit. So type is (DataFrameReader, SparkSession) => Unit

2. () => (new ProcessorOne()).process is function. It takes nothinks () and returns function from 1). So type is () => (DataFrameReader, SparkSession) => Unit

3. new ProcessorOne().process() is funcation call. If you use .process() then you call funcation without params. If you use .process then you return link to function

You could learn more about this from Official docs or Scala exercises

trait Processor {
def processOne(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit
def processTwo(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit
}

class BMValsProcessor extends Processor {
def processOne (oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit = {
println("in BMValsProcessor processOne ") ///actual business logic
}
def processTwo (oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit = {
println("in BMValsProcessor processTwo ") ///actual business logic
}
}

class BMValsProcessor2 extends Processor {
def processOne(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit = {
println("in BMValsProcessor2 processOne") ///actual business logic
}
def processTwo(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit = {
println("in BMValsProcessor2 processTwo") ///actual business logic
}
}

object ValProcessor {
def main(args: Array[String]): Unit = {

val df: DataFrameReader = null; // initialization of DataFrameReader
val spark: SparkSession = null; // initialization of SparkSession

val procs: Map[String, (DataFrameReader, SparkSession) => Unit] = getAllDefinedProcessors()

procs.values.foreach(
  proc => proc(df, spark)
)

}

def getAllDefinedProcessors(): Map[String, (DataFrameReader, SparkSession) => Unit] = {

Map(
  "bm_vals" -> new BMValsProcessor().processOne,  /// How to register/point and call processTwo
  "bm_vals2" -> new BMValsProcessor2().processOne /// How to register/point and call processTwo
)

}

}

You could try something like

trait Processor {
  def processOne(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit

  def processTwo(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit
}

class BMValsProcessor extends Processor {
  def processOne(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit = {
    println("in BMValsProcessor processOne ") ///actual business logic
  }

  def processTwo(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit = {
    println("in BMValsProcessor processTwo ") ///actual business logic
  }
}

class BMValsProcessor2 extends Processor {
  def processOne(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit = {
    println("in BMValsProcessor2 processOne") ///actual business logic
  }

  def processTwo(oraOptionDfConfig: DataFrameReader, sparkSession: SparkSession): Unit = {
    println("in BMValsProcessor2 processTwo") ///actual business logic
  }
}

object ValProcessor {
  def main(args: Array[String]): Unit = {

    val df: DataFrameReader = null; // initialization of DataFrameReader
    val spark: SparkSession = null; // initialization of SparkSession

    val procs: Map[String, Processor] = getAllDefinedProcessors()

    procs.values.foreach {
      proc =>
        proc.processOne(df, spark)
        proc.processTwo(df, spark)
    }
  }

  def getAllDefinedProcessors(): Map[String, Processor] = {

    Map(
      "bm_vals" -> new BMValsProcessor(), 
      "bm_vals2" -> new BMValsProcessor2() 
    )
  }

}