Preheat the oven to 350 F. In a medium bowl, whisk together flour, salt, and baking soda. In a large bowl, combine butter with peanut butter and both sugars until smooth.
Add in the egg and vanilla extract, and mix until smooth. Add in the flour mixture, and mix until it is fully combined. Roll the cookie dough into balls, and place at least 2-inches apart onto ungreased baking sheets.
Bake for 10-12 minutes. Remove from the oven, and top each cookie with one unwrapped Rolo.