In a large mixing bowl, using an electric mixer, beat the softened butter, peanut butter and both sugars until light and creamy.
Add eggs one at a time, beating on low speed after each egg is added.
Beat in the vanilla, salt and baking soda, then add the flour and stir until it is fully blended.
Stir in the peanut butter chips.
Using a large cookie scoop or a ¼ cup measure, scoop up mounds of cookie dough and place on a couple of plates or small tray (something you can fit in the refrigerator) lined with plastic. Cover the scooped mounds and chill for two hours or until ready to bake.
When ready to bake, heat oven to 350 degrees. Line large cookie sheets with parchment paper, or use ungreased cookie sheets.
Arrange the chilled mounds on baking sheets spacing 3 inches apart. Press a few peanut halves into each cookie if desired.
Bake at 350 degrees for 15 to 17 minutes or until the edges are very lightly browned and the centers seemed cooked bust still soft.
Remove from oven and let cookies rest on the sheet for a couple minutes before transferring to wire racks to cool.
Notes
If you aren't using a scale and are measuring by volume, make sure to really aerate the flour before measuring and measure with a light hand. It's best to just weigh it.