1. Make the biga by combining 1/2 cup warm water (105 degrees) and 1/16 teaspoon of active dry yeast in a mixing bowl and give it a few minutes for the yeast to dissolve. Once the yeast has fully combined with the water, add in the 1/2 cup flour. Mix to combine. Cover the blow with plastic wrap and leave 12-24 hours to ferment. Once done the biga will be bubbly and look like pancake batter. 
2. Once the biga is ready, put it in a bowl fitted to a stand mixer with the dough hook attachment. Add the 1 and 1/4 cup warm water, 1/4 cup olive oil, and the rest of the yeast and mix well. While on low speed, slowly mix in the 3 1/4 cups flour until fully combined. 
3. Add the salt, turn the speed up to medium, and beat the dough until it has formed enough gluten. About 5-10 minutes. 
4. Let the dough rise by placing it in a large bowl greased with olive oil. Cover with plastic wrap and leave it until it has doubled in size, 1 1/2 -2 hours. 
5. Once the dough has doubled in size, pour it out onto a floured surface and stretch the dough by pulling each side of the dough and folding it to the center. Put the dough back into the bowl folded side down and cover with plastic wrap and let it rise until it has doubled in size again. About 1 more hour. 
6. Pour 1/2 cup olive oil into 2 10″ baking tins and push it around to coat the pans fully. Divide the dough into 2 equal pieces and place each piece into a tin. Cover the pans with a tea towel and let the dough rest for 3o minutes.
7. Once rested, add the onions, the brown butter, and sage. Gently them into the dough so that it all becomes well dispersed. Cover and let it rest for 45 minutes more. While it rests preheat the oven to 400 degrees. 
8. Bake the dough for 30-40 minutes until crust is golden and very crispy. Brush baked focaccia with olive oil and sprinkle with more sea salt. 

For the onions:

1. Heat the 3 tablespoons olive oil and 1 tablespoon butter in a large saucepan on medium-high heat. 
2. Add the onions and cook until all the onions have softened. Be sure to stir continuously so that they don't start to burn. 
3. Once softened and the sugar, reduce the heat and cook until the onions are brown and thoroughly caramelized. 30 minutes -1 hour. 

For the brown butter sage:

1. Heat 8 tablespoons butter on medium-high heat until it's completely melted. 
2. Add the sage and cook until the butter has turned a light amber color and little brown bits have formed in the pan.