Combine warm water, honey, and active dry yeast in a large mixing bowl. Whisk briefly and allow to stand for 10 minutes until the mixture is foamy.
Add the bread flour and fine sea salt to the yeast mixture. Stir using a sturdy spatula until a sticky, shaggy dough forms and no dry streaks remain.
Drizzle 2 tablespoons of olive oil over the dough. Cover the bowl tightly and allow to rise in a warm environment for 60 minutes or until the volume has doubled.
Generously grease a 12-cup standard muffin tin with olive oil, allocating approximately 1 teaspoon per cup to ensure the bottoms fry to a golden crisp.
Gently deflate the dough and divide into 12 equal portions (approximately 55-60g each). Place one portion into each muffin cup, cover, and let rise for another 45 minutes.
Prepare the aromatic topping by heating 1/3 cup olive oil, minced garlic, and rosemary in a small saucepan over medium-low heat. Infuse for 2-3 minutes until fragrant but before the garlic browns; remove from heat immediately.
Preheat the oven to 450°F (230°C).
Lubricate your fingertips with oil and press deep dimples into each muffin, reaching the bottom of the tin. Distribute the infused garlic-rosemary oil evenly across all 12 muffins.
Bake for 18-20 minutes or until the tops are deeply golden and the edges appear crispy and pulled away from the tin.
Remove from the oven and immediately brush the tops with melted butter. Finish with a generous sprinkle of flaky sea salt. Rest in the tin for 5 minutes before transferring to a cooling rack.