Preheat the oven to 375° F. Line a large baking sheet with parchment paper or a Silpat mat.
Mix together the flour, baking soda, salt and baking powder in a large bowl. Hold this aside.
Cream together the softened butter, granulated sugar and brown sugar in the bowl of a stand mixer or in a large bowl with a hand mixer. Cream the butter and sugars for about 5 minutes. Mix in the eggs one at a time, then add the vanilla extract and mix this in, too. Beat in the peanut butter until the mixture is smooth.
Add the flour mixture to the bowl in two additions, scraping the bowl a couple of times to be sure everything is incorporated.
Scoop out portions of the dough using a tablespoon-sized cookie scoop and space them evenly on the prepared baking sheet. Press a small indentation in middle of each dough portion with your thumb (not too deep.)
Bake the cookies for 10 minutes. While this batch bakes put the bowl of remaining dough in the fridge to keep it chilled.
After 10 minutes pull the baking sheet from the oven and set a caramel into the center of each cookie, pressing it in just a little.
Bake the cookies for an additional 4-5 minutes until the edges are lightly browned. Pull the pan from the oven, let the cookies rest on the pan for 10 minutes, then carefully transfer them to a cooling rack with a spatula. (If they seem too fragile let the rest a little longer. If you used parchment paper you can also carefully lift the paper and cookies up by grabbing opposing corners and quickly move the whole thing to the cooling rack.)
Repeat the baking and caramel steps with the rest of the dough. Once the baked cookies have cooled, store them in a sealed container at room temperature for up to 4 days. Makes about 36 cookies.
Don't skimp on the quality of the caramels. (I found out the hard way on this one.) The candies get tucked into the cookie centers a few minutes before they come out of the oven - just enough time to melt. And rock-hard, cheap caramels will not melt. Use a good brand of soft caramels.