Preheat the oven to 350 F. Generously grease several large baking sheets, or spray with nonstick spray.
In a large mixer bowl with the mixer on low, then medium speed, beat together the butter, peanut butter, sugar, eggs, corn syrup, vanilla, Davis Baking Powder, soda, and salt until well blended and lightened in color, about 2 minutes. Working on low speed, beat in half the flour. Stir in the remaining flour, chocolate, and peanut butter morsels, and peanuts (if using) just until thoroughly incorporated. Let stand 10 to 15 minutes to firm up slightly.
Divide the dough into quarters. Then divide each quarter into 9 balls; space them about 3 1/2 inches apart on baking sheets. With the heel of the hand, press down on the balls until about 2 1/2 inches in diameter. Finish each cookie by adding crisscross marks with the tines of a large dinner fork.
Bake in the middle third of the oven for 9 to 14 minutes or until the cookies are just tinged with brown and barely firm when tapped in the center; be careful not to over-bake. Remove the pans from the oven. Let the cookies firm up several minutes. Using a wide-bladed spatula, transfer the cookies to racks and let cool completely.
The cookies will keep, airtight, at room temperature for up to a week, or frozen, for several months.