Beat butter and brown sugar together in a bowl with a mixer on medium speed. Mix in molasses, then egg, until blended, scraping bowl as needed.
In a small bowl, combine flour, baking soda, salt, ginger, 1 tsp. cinnamon, cloves, nutmeg, and pepper; add to butter mixture on low speed, mixing until combined.
Divide dough in half, shape each into a disk, wrap in plastic wrap, and chill until firm, about 3 hours. Meanwhile, in a small bowl combine remaining 1/2 tsp. cinnamon with granulated sugar; set aside.
Preheat oven to 350°. Pull off about 1 tbsp. of dough from disk, roll into a ball, and drop into cinnamon sugar bowl. Working in batches of 3 or 4, coat dough balls in sugar and arrange about 1 in. apart on parchment-lined baking sheets.
Bake cookies until dry-looking and just starting to brown on edges, about 8 minutes. Set pans on racks and let cookies cool on pans.
Make ahead: Chill dough (step 3) up to 1 week. Store baked cookies airtight up to 3 days.
Note: Nutritional analysis is per cookie.