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
    )
  }

}

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() 
    )
  }

}