Place sliced peaches in a medium bowl and stir in 1/2 cup sugar. Stir well and cover with plastic wrap. Place in refrigerator until ready to use.
Preheat oven to 425º.
In a medium bowl, combine Bisquick, milk, 3 tablespoons sugar and butter. Stir with a wooden spoon just until everything is incorporated and a soft dough forms.
Scoop out dough onto an ungreased baking sheet, making about 6 drop biscuits. Sprinkle with coarse sugar, if desired.
Bake 12 to 15 minutes or until shortcakes are golden brown. Remove from oven and cool for about 5 minutes on the pan.
Remove from pan with a spatula onto serving plates.
Cut the shortcakes in half to make a top and a bottom. Spoon a generous portion of sweetened peaches over the shortcake bottoms. Cover with shortcake tops.
Serve with fresh whipped cream or ice cream.