I'm way too happy that I was able to get this to work (specifically OMGThatsUseful.soAmaze)

whatdothetypessay.scala

sealed abstract class BaseClass {
  def name: String
  def someData: Option[Int]
}

trait NamedThing extends BaseClass {
  def name: String
}

trait WhatDoTheTypesSay[This <: NamedThing] {
  def setSomeData(i: Int): This
}

case class Herp(name: String = "this one", someData: Option[Int] = None)
    extends BaseClass
    with NamedThing
    with WhatDoTheTypesSay[Herp] {

  def setSomeData(i: Int) = copy(someData = Some(i))
}

case class Derp(name: String = "that one", someData: Option[Int] = None)
    extends BaseClass
    with NamedThing
    with WhatDoTheTypesSay[Derp] {

  def setSomeData(i: Int) = copy(someData = Some(i))
}

object OMGThatsUseful {
  def soAmaze[T <: NamedThing](bc: WhatDoTheTypesSay[T]): BaseClass = {
    bc.setSomeData(42)
  }

  def callThat(): Seq[BaseClass] = {
    val herp = Herp()
    val derp = Derp()
    Seq(soAmaze(herp), soAmaze(derp))
  }
}