Roasted Garlic-and-Caramelized Onion Focaccia Rolls

For garlic: In a small saucepan, place garlic. Add enough olive oil to submerge garlic. Bring to a boil over medium heat; reduce heat, and simmer, stirring frequently, until garlic is very soft, about 30 minutes. Let cool completely.

Crush roasted garlic in oil; transfer mixture to a resealable jar, and refrigerate for up to 2 weeks.

For onions: In a small skillet, melt butter over medium heat. Add onion, sugar, and kosher salt; cook, stirring frequently, until onion is soft and translucent, about 10 minutes. Reduce heat to medium-low; cook, stirring frequently, until golden brown, 25 to 35 minutes. Let cool completely. Refrigerate in an airtight container for up to 3 days.

For dough: In the bowl of a stand mixer, combine 1 cup plus 3 tablespoons (270 grams) room temperature water and 1½ tablespoons (21 grams) extra-virgin olive oil. Add flour, kosher salt, and yeast. Using the paddle attachment, beat at low speed until combined, about 1 minute; scrape sides of bowl and paddle. Beat at medium-low speed until dough pulls away from sides of bowl and forms a smooth ball on paddle, 3 to 4 minutes, stopping to scrape sides of bowl.

Oil a large bowl. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) for 1½ hours, folding dough in bowl every 30 minutes. (To fold, use wet or oiled hands to reach under one side of dough; gently stretch up, and fold over center. Repeat 3 more times around bowl.)

Spray a 12-cup muffin pan with cooking spray.

Turn out dough onto a lightly floured surface, and divide into 12 portions (about 58 grams each). Place each portion into a prepared muffin cup. Cover with plastic wrap, and let rise in a warm, draft-free place (75°F/24°C) until puffed and dough just reaches top of muffin cups, about 20 minutes.

Preheat oven to 425°F (220°C).

Drizzle remaining 1½ tablespoons (21 grams) extra-virgin olive oil onto rolls. Using your fingers, dimple dough, touching pan through dough without tearing dough.

Dot or spread about 1 crushed roasted garlic clove on each roll. Season with sea salt (if using).

Bake until tops are lightly browned and almost set, about 5 minutes. Top rolls with caramelized onion as desired. Bake until rolls are golden brown and an instant-read thermometer inserted in center registers 190°F (88°C), 6 to 7 minutes more. Let cool in pan on a wire rack for 10 minutes. Brush warm rolls with oil from roasted garlic. Garnish with rosemary, if desired. Serve warm. Store in an airtight container for up to 3 days.