Mix flour, sugar, baking powder and salt together in a large bowl. Cut in butter with a pastry blender or two knives until mixture resembles coarse crumbs. Beat eggs, milk and vanilla extract together in a small bowl. Stir into dry ingredients with a fork until dough comes together. Knead a few times in the bowl to moisten all ingredients. If sticky, add a little more flour. If too dry, add a bit more milk. Shape dough into a disk and wrap in plastic wrap. Refrigerate for about 1 hour.