In a large bowl, dissolve the honey in the warm water. Sprinkle the yeast over the top and let sit for 5-10 minutes until foamy.

Add 2 tablespoons of olive oil, fine sea salt, and the flour to the yeast mixture. Mix with a sturdy spoon until a shaggy, sticky dough forms. Ensure no dry flour remains.

Cover the bowl with a damp towel or plastic wrap. Let the dough rise in a warm place for 1 to 1.5 hours until doubled in size and bubbly.

Generously coat each cup of a 12-cup muffin tin with extra virgin olive oil (about 1/2 tsp per cup), greasing the bottoms and sides thoroughly.

With lightly oiled hands, gently deflate the dough. Divide it into 12 equal portions. Drop one portion into each prepared muffin cup.

Cover the muffin tin loosely and let the dough rest for a second rise, about 45 minutes to 1 hour, until the dough puffs up to fill the cups.

Preheat your oven to 400°F (200°C). In a small bowl, mix the remaining olive oil with the minced garlic and fresh rosemary.

Drizzle the garlic-rosemary oil evenly over the puffy dough in the tins. Oil your fingers and press firmly into the dough in each cup, pressing all the way to the bottom to create deep dimples.

Sprinkle the tops generously with flaky sea salt. Bake in the preheated oven for 18 to 22 minutes, or until the muffins are deep golden brown and crispy on the edges.

Let cool in the pan for 5 minutes before transferring to a wire rack to prevent soggy bottoms. Serve warm.