Preheat oven to 425°F. Line a large baking sheet with parchment. Sift cocoa, flour, baking powder, baking soda, salt and 1/4 cup sugar into a large bowl. Add butter and rub in with fingertips until mixture resembles coarse meal.
Stir in milk until a rough dough forms. Do not overmix. Divide dough into 4 equal portions (a heaping 1/3 cup each). Gently shape into mounds; sprinkle tops with sugar. Transfer to baking sheet and bake until a toothpick inserted into center comes out clean, 12 to 14 minutes. Transfer biscuits to a wire rack and let cool.
Toss strawberries and 1/4 cup sugar in a bowl. Let stand at room temperature, stirring occasionally, until juices form, about 30 minutes. Using a hand mixer on high, whip cream and 2 Tbsp. sugar in a large bowl until soft peaks form.
Using a serrated knife, slice each biscuit in half horizontally and place 1 bottom half on each of 4 plates. Spoon 1/4 of berry mixture on each bottom. Dollop with whipped cream and top with remaining biscuit halves. Serve immediately.