Preheat the oven to 375 F.

Wash and peel the peaches. Cut them into 1" pieces and place them at the bottom of a 7×11 casserole dish. Stir in the remaining filling ingredients so that the peaches are fully coated. Bake the filling for 10 minutes. Remove from the oven and set aside.

In a separate mixing bowl, combine flour, sugar, baking powder, baking soda, and salt. Add the butter in small cubes and mix it in with the dough using your fingers until small pea-sized pieces have formed. Add non-dairy milk and stir together until a stiff dough has formed. You may need to add a little more milk. If so, add it 1-2 teaspoons at a time.

Drop pieces of dough onto the peach filling so that it is mostly covered with a large piece of dough. Brush additional non-dairy milk over the drop biscuits and sprinkle with coarse sugar.

Bake for 45-60 minutes, uncovered until the filling is bubbling up and the biscuits are golden brown. Remove from the oven and let sit for 20 minutes before serving.