To make the Sticky Peanut Butter Cookies, first cut the butter into chunks and beat with the whisks of a hand mixer or food processor until creamy, gradually adding the brown sugar and sugar. Then thoroughly mix in the peanut butter first, then the egg and vanilla extract.
Combine flour, baking soda and 2 pinches of salt and stir in briskly. Form the dough into about 30 small balls each around a rolo. Place the balls on baking sheets lined with parchment paper, spacing them generously apart, and press them crosswise with a fork to flatten and round them 1-1 1/2 inches high. Refrigerate for 30 minutes.
Preheat the oven to 175 °C top/bottom heat (160 °C convection oven). Bake the Sticky Peanut Butter Cookies in the oven (center) for about 10 minutes until lightly brown. Remove and let cool on the tray.