Whisk together the flour, sugar, baking powder, baking soda, and salt, and drop in the cubed butter. Put the bowl in the freezer and leave it there for 30 minutes. Bag your berries or lay them on a sheet pan and also freeze for up to 30 minutes. This will help keep the berries distinct and from mashing into your cookie batter.
Meanwhile, adjust the oven rack to the middle position and preheat the oven to 375°F.
Line a baking sheet with parchment paper or spray with nonstick spray.
Using a pastry cutter or a fork, work the chilled ingredients together in the bowl until the butter cubes are the size of peas. Make a well in the center. Combine the vanilla and milk in a separate bowl, and pour the mixture into the well. Mix the ingredients with a spoon to form a shaggy, slightly crumbly mass. Let stand for 3 to 5 minutes to let the flour absorb the liquid, then fold one more time. If the dough seems simply too dry to come together, add 1 tablespoon milk at a time until it just barely comes together.
Add the frozen berries and gently mix them in.
Using a spoon, scoop the batter on baking sheet about 1 inch apart. Or you could spread the batter across the baking sheet and slice the cookies when ready to serve.
Bake for 10-15 minutes until the center is still soft and the edges are golden brown.