Melt the butter in a large microwave-safe bowl and let it cool to room temperature to avoid greasy cookies.
In a large bowl, combine the flour, cream of tartar, salt, baking soda, and ground cinnamon.
In a separate bowl, mix the cooled melted butter with both sugars. Whisk until blended. Add the egg, egg yolk, and vanilla, whisking until smooth.
Combine dry ingredients with the wet ingredients until no flour streaks remain, avoiding over mixing. Cover the dough and chill for 1 hour.
Preheat oven to 325°F (163°C). Stir together the white sugar and cinnamon in a small bowl.
Portion the dough into roughly 2 tablespoons pieces. Encase a Rolo in each, shape into tall balls, and roll in cinnamon-sugar. Chill for 15–20 minutes until firm.
Place dough balls on a lined sheet pan, spacing about 6 apart with ample spacing between each. Bake for 9–12 minutes, aiming for slight underbaking. After baking, if cookies have uneven edges, press them inwards with a metal spatula. Let them sit on the tray for 5 minutes before moving to a cooling rack.
Notes
Note 1: Accurate flour measurement is vital, too much makes dry cookies and too little causes spreading. Use a kitchen scale and aim for 395 grams of flour for this recipe. Storage: Store cookies in an airtight container at room temperature for 2–3 days or freeze the dough for up to 3 months. To freeze, form the dough around caramels, roll in cinnamon sugar, and freeze on pan. Then, move frozen balls to an airtight container or bag. You can bake frozen dough without thawing, just adjust time as needed so that edges are set, and the center is soft.