MICROWAVE milk until warm, 45 sec. Pour into bowl of a stand mixer fitted with dough hook. Add yeast and stir. Let stand for 5 min.
ADD flour, 2 tbsp butter and salt. Beat on medium-low until dough forms a ball and is very smooth, about 5 min.
SPRAY a medium bowl with oil. Line a large baking sheet with parchment. Lightly spray with oil.
SCRAPE dough out of mixer bowl into oiled bowl. Lightly oil top of dough and cover with a damp tea towel (not terry cloth). Let stand in a warm place until dough doubles in size, about 1 hour.
DIVIDE dough into 8 portions. Roll each into a ball, then arrange on prepared sheet. Cover with same damp tea towel and let stand, 15 min.
ROLL out each portion on a floured surface into 1/8 in. thick ovals. Transfer to prepared sheet. Cover with same damp tea towel and let stand, 15 more min.
POUR oil into a large pot until it reaches 1 in. up the sides (about 6 cups). Clip a deep-fry thermometer to the side. Heat over medium until temperature reaches 325F. Adjust heat as necessary to keep temperature at 325F during cooking. Fry dough, 1 piece at a time, flipping often, until golden, 2 to 3 min. Drain on paper towels.
STIR coconut sugar with cinnamon on a plate until combined. Brush tops and bottoms of “snowshoes” with 1/4 cup butter.
DIP both sides into sugar until well coated. Serve with lemon wedges.