Preheat oven to 350°F (175°C). Grease a 9"x 13"x 2" baking pan.
Whisk together the flour, baking powder, and salt. Set aside.
Using an electric mixer on medium speed, beat the butter and brown sugar until thoroughly combined. Add the eggs and vanilla, and mix well.
Reduce mixer speed to low. Gradually add the flour mixture, mixing just until combined.
Stir in the caramel bits and peanuts.
Transfer the batter to the prepared pan, and spread evenly. If desired, a pinch or two of coarse salt over the top of the batter.
Bake 35 to 40 minutes, or until the edges are browned and the center appears set. A pick inserted into the center should come out with a few moist crumbs attached.
Cool completely in the pan before cutting into bars.
Notes
With the salt on top of these bars, I prefer to use unsalted peanuts. If you use salted peanuts, I recommend either reducing the amount of salt in the recipe or omitting the sprinkling of salt on top.