Preheat oven to 375 degrees.
Combine flour, salt, and baking soda in a medium-sized bowl and set aside.
Beat the two softened sticks of butter, the sugar and brown sugar, and vanilla in a large bowl until it is creamy.
Add eggs one at a time, beating the mixture well after each egg.
Gradually beat in the flour mixture.
Using mini muffin tins, drop 1 1/4 inch balls into each cup.
Bake for 7-9 minutes only. Cookies will appear raw, but they aren't.
Unwrap peanut butter cups and press them into the center of the hot cookie.
Let them cool for 5 minutes and remove to cooling rack.
There will be exactly enough dough for 48 cookies.