Roast the garlic. Preheat oven to 400F. Cut heads of garlic in half, then place in a baking pan with olive oil. Cover with aluminum foil then roast for 45 minutes, until garlic is very soft. Let cool.
Squeeze out the garlic. Gently squeeze the heads of garlic to push out individual garlic cloves (it’s fine if they are mushy and lose their shape). Place in a mall bowl. Reserve garlic olive oil.
Activate the yeast. In the bowl of a stand mixer fitted with dough hook, combine 1¾ cups warm water,1 package active dry yeast and 1 Tbsp sugar. Let sit for 10 minutes to activate yeast.
Make the focaccia dough. Add 4½ cups bread flour, 1 Tbsp Kosher salt, and ½ cup of reserved garlic olive oil, then mix on low speed until dough comes together. Increase speed to medium and mix for 6-8 minutes, or until dough goes from sticky to elastic, but smooth.
Let the dough rise. Pour a few tablespoons of reserved garlic oil in a large mixing bowl, then place dough inside. Turn dough over, coating it on all sides with the oil. Cover loosely with a kitchen towel, then place in a warm spot for at least 1 hour or up to 2 hours, until dough has doubled in size.
Fold the dough. Pour ¼ cup of remaining garlic oil in an 13"x18" rimmed baking sheet. Place dough on baking sheet, then carefully stretch and fold the right side of the dough up and over towards the center. Repeat with remaining 3 sides of dough (top to bottom, left to right, then bottom to top. Turn down over so it is seam side down, then let rest for 10-15 minutes.
Dimple the dough. Carefully press the dough with your finger tips - creating deep dimples in the dough - to stretch and shape it to fit the pan. If the dough resists and bounces back, let it sit for another 10 minutes.
Chill overnight. When the dough is fully formed to the pan, cover with oiled plastic wrap, then place in a refrigerator to cool at least 8 hours or overnight.
Bake the focaccia. Remove dough from refrigerator, uncover, and place in a warm place for 2 hours. When ready, preheat oven to 425F. Stud dough with all garlic cloves, then sprinkle with sea salt. Bake for 20 minutes, then remove and evenly distribute sun-dried tomatoes on top. Bake for additional 3 minutes, then remove and let cool. Cut into slices and serve warm or at room temperature.