2 large South Carolina sweet onions (approximately 2 1/2 lbs.)
5 Tbs. extra-virgin olive oil, divided
1/2 tsp. kosher salt
4 garlic cloves
1/2 cup chopped basil
1/2 cup chopped cilantro
Juice of 2 lemons
Juice of 2 limes
1/2 cup extra-virgin olive oil
Peel the onions and cut them into 1/4-inch even slices, yielding approximately eight loose cups. Heat four tablespoons of olive oil in a heavy-bottomed pot over medium heat. Add onions and salt and stir to combine. As onions begin to brown, stir frequently. Add small amounts of water if the caramelizing onions begin to stick. Continue to cook onions, stirring frequently, until they are dark brown and sweet smelling, 30 to 40 minutes. Remove from heat. You should have two cups of caramelized onions. Cool to room temperature.
Slice jalapeños in half lengthwise, remove the seeds, and slice halves in half. Peel garlic and thinly slice it. Heat remaining one tablespoon olive oil in a skillet over medium heat until it shimmers. Add jalapeños and cook them, turning, until the skin sides blister, about two minutes. Add the garlic and cook, stirring frequently, until it is golden brown, about 30 seconds. (Be careful not to burn the garlic.) Add the jalapeños and garlic to the caramelized onions. You can make the sauce up to this point several hours ahead. Cover and keep at room temperature.
When ready to serve the sauce, bruise the herbs with a mortar and pestle. Add the herbs, lemon and lime juices, and olive oil to the caramelized onion mixture. Serve immediately over red drum or tile fish.