Heat milk to 115°F. Dissolve yeast and 1 tsp sugar in warm milk. Allow to proof for 5-10 minutes. 

Add remaining dough ingredients to the bowl of a stand mixer with dough hook attachment. With mixer running on low, pour in yeast mixture. Increase speed and mix until dough comes together and forms a ball. 

Transfer dough to a greased bowl. Cover and allow to rise in a warm location until doubled in size, roughly 1 hour. 

Preheat vegetable oil to 350°F in a deep fryer or large stockpot. 

Prepare a large baking sheet with a silicone mat or parchment paper, sprinkle well with flour.

Flour a silicone counter mat or work station well with flour. Sprinkle top of dough with flour. Roll out to 1/4 and 1/2-inc thickness. Use a 3-4-inch donut cutter. A biscuit or cookie cutter may be used in place of a donut cutter. Transfer cut donuts to prepared baking sheet. 

Fry donuts in batches until golden brown. Cook for 2-3 minutes, flipping halfway through. Drain and cool on paper towels. 

Melt butter and brown sugar in a small saucepan over medium heat. Stir well to combine. Add in maple syrup and milk. Whisk well to combine. Bring to a low boil. Whisk in powdered sugar, cooking until fully combined and thickened. Carefully tops of donuts in warm sauce. Transfer to a cooling rack. Repeat with remaining donuts, whisking sauce as needed between donuts. 

Allow glaze to cool and harden before serving.