Preheat oven to 400 degrees F.
Cut the lemons in half and pick out the seeds and discard. Lightly coat the lemons with 1 tablespoon of olive oil. Place lemons cut side down in a baking dish and roast, uncovered, for 25 minutes. Remove from oven and let lemons cool; discard any juice and oil from the bottom of the baking dish.
Once the roasted lemons are cool, cut off ends of the lemons and then cut the lemons into a small 1/4-inch dice (make sure you capture and save all the pulp and juice that comes out of the lemons as you dice them). NOTE: I find it easier to cut the lemons into thin strips and then cut into the small dice.
In a bowl, combine the lemons (with juice and pulp), the remaining olive oil, shallots, sugar, and salt; stir gently. Cover and set aside for at least 3 hours so the flavors can marry and mellow. NOTE: Initially, the lemons may seem harsh or bitter, but as they sit, their flavor changes markedly. Taste a couple of times throughout the rest period, and you will start tasting the difference.
Place lemon salsa mixture in the food processor. Add basil pesto and process on grind setting (stopping and stirring mixture a few times). Adjust seasonings with additional salt, pepper, and additional lemon juice (if desired).
Store covered in the refrigerator for up to a week.
Yield: 1 1/2 cups.
* Commercially grown citrus fruits are coated with a wax that gives it a nice shine and helps extend shelf life - fruits do not dry out as quickly when waxed. Although it is food-grade wax, none of us needs to consume it. The best way to remove it is to use a mild detergent solution and a clean pot-scrubber sponge and then rinse thoroughly.
Roasted Lemon Salsa Recipe: https://whatscookingamerica.net/appetizers/roastedlemonsalsa.htm