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Heat the milk to 100 degrees F; make sure it doesn't get too hot or it will kill the yeast. Add the sugar to the milk and whisk until dissolved. Add the yeast and whisk to combine, then transfer the mixture to a stand mixer fitted with the bread hook.
On the lowest speed, add half of the flour and mix until evenly combined. Add the salt and egg yolks and mix until fully incorporated. Slowly add half of the melted butter and mix until incorporated. Add half of the remaining flour and mix to combine, scraping down the mixing bowl with a rubber spatula. Add the remaining melted butter followed by the remaining flour and mix for 15 minutes. Cover the mixer bowl with plastic wrap and proof until the dough is "pillowy," about 30 minutes.
Preheat the oven to 350 degrees F and line a baking sheet with parchment paper.
Measure out 15 ounces of the kolache dough (reserve the remaining dough to make Fresh Fig and Speck Kolache). Divide the dough into six 2 1/2-ounce rounds. Wrap a piece of dough around each piece of sausage and transfer to the prepared baking sheet. Proof for 10 minutes, then bake until golden brown, about 20 minutes. Serve warm.