Preheat the oven to 500 degrees Farenheit (yes, really!) Line a quarter-sheet pan or a 9x13 pan with parchment paper, then lightly grease it. Set aside.
In a large mixing bowl, whisk oats, rye and all-purpose flours, baking powder, baking soda, salt, and sugar, until fully combined.
Add the butter in chunks and use a pastry cutter or two forks to cut the butter into the dry ingredients until the mixture is a coarse texture and the butter is mostly incorporated.
Add the sourdough starter to the bowl and cut this in with the pastry cutter as well. It's okay if it's not fully incorporated, it will be when you add the milk.
Add the milk to the mixing bowl and stir- a dough whisk or a spatula will work well. This is a very wet, sticky dough!
Scrape the dough into the prepared pan. Use wet hands to gently spread it out to evenly fill the pan.
Optional: let the dough rest on the counter for 30 minutes, or in the fridge for a few hours for a little more "spring" to the bread. The longer you leave it, the more the flavor will "sour" like sourdough as the discard will begin to ferment the bread.
Bake for 12-15 minutes, until lightly browned and springy to the touch. Allow to cool for 10 minutes in the pan, then cut into squares and serve warm.
Notes
1. If you prefer, you can substitute barley flour for the rye- they are both traditionally used in rieska!