Heat oven to 375° F.
In a large bowl, combine the flour, baking powder, salt, and sugar. Using a pastry blender, a fork, or your fingertips, add the butter and combine until the mixture resembles coarse meal. Add the thyme and toss.
In a measuring cup, whisk together the milk and mayonnaise. Add to the flour mixture and stir just until combined. Turn the dough onto a lightly floured work surface and pat into a rectangle about 1 inch thick. Cut the biscuits into squares. Transfer to a baking sheet and bake until lightly browned, about 25 minutes. Serve hot.