Preheat the oven to 350 degrees Fahrenheit.
Place the garlic cloves and olive oil into a tiny roasting pan. The pan should be small enough where the garlic cloves are completely submerged under the olive oil.
Tightly wrap the top of the roasting pan with a piece of plastic wrap and then a piece of tin foil. Set this on the middle oven rack and roast it for 1 hour.
Once the roasted garlic has cooled down somewhat, remove it from the olive oil and place it into a small bowl. Mash the garlic with a fork to turn it into a slightly chunky puree. Do NOT dump out the garlic olive oil. Set both aside.
Now, add the yeast, sugar, and warm water into a standing mixer bowl. Quickly stir and then allow resting for 10 minutes. The mix should be very frothy after resting.
To the yeast mixture, add in the roasted garlic puree, 1/4 cup of the garlic oil, flour, and kosher salt. Knead this with the dough hook attachment at the lowest speed. Stop the mixer and scrape down the sides and underneath the mixture of the bowl, as needed.
Once everything has combined, set a timer for 5 minutes and continue kneading over the lowest speed.
Lightly grease a large mixing bowl with some olive oil. Scrape the dough into the bowl and toss it around to coat it in the oil. Smooth a piece of plastic wrap directly on top of the dough and then wrap the top of the bowl in plastic as well. Set this in a dark warm place to rest for 1 hour.
Grease a 9"x13" non-stick sheet pan with 1 tablespoon of the garlic oil.
Dump the dough onto the greased pan and press it evenly across, from corner to corner.
Rest a sheet of plastic wrap over the dough and let it rise for 30 minutes.
Preheat the oven to 425 degrees Fahrenheit.
Take your hands and generously press all of your fingers over the entire dough, creating dimples everywhere. Don't be shy with this step! Press your fingertips down to touch the bottom of the pan. However, do not make any actual see-through holes.
Now, evenly drizzle over another 1/4 cup of the garlic oil. Then, evenly sprinkle over the rosemary leaves and flakey sea salt.
Set the baking sheet on the middle oven rack and then bake the focaccia for 15-18 minutes, rotating the pan half-way through. The focaccia should be a light-medium golden brown in the end.
Drizzle the last bit of the garlic oil all over the focaccia.
Cut it twice vertically and three times horizontally to give you 12 pieces of focaccia.