Sift together flour, baking soda, and salt. Set aside.
Using an electric mixer, beat butter, granulated sugar, and brown sugar until fluffy. Add eggs, one at a time, beating well after each addition. Add vanilla and peanut butter. Beat until combined.
Add half of flour mixture. Mix for 15 seconds. Add remaining flour mixture and mix just until combined. Fold in chocolate. Cover bowl and refrigerate for at least 3 hours.
Preheat oven to 375°. Line baking sheets with parchment paper or silicone liners.
Drop dough by rounded tablespoonfuls onto baking sheets, leaving about 2 inches between cookies. Using the palm of your hand, gently press each cookie down so that it forms a tall disk shape. Be sure not to press too hard or press cookies too flat.
Sprinkle tops of cookies with granulated sugar or sanding sugar. Bake 10-12 minutes, until tops of cookies just begin to brown.
Cool cookies on pan on wire rack for 5 minutes. Transfer cookies to rack to cool completely. Store in an airtight container for up to 3 days.
Makes about 24 cookies.