In a medium bowl, whisk together flour, salt, and baking soda. In a large bowl with a mixer, beat softened butter with peanut butter and both sugars.
Add in egg and vanilla extract, beat until smooth. Add the flour mixture in three additions, beating after each until fully incorporated. Cover and refrigerate for at least one hour.
Preheat oven to 350 F. Divide cookie dough into pieces, flatten slightly, place one rolo on each dough and roll into a ball. Place cookies at least 2-inches apart onto ungreased baking sheets. Bake for 10-12 minutes.
