Add the tomatoes, shallot, capers, basil, 2 Tbsp of the olive oil, & aged balsamic vinegar to a bowl. Season with 1/2 tsp S&P or crushed red pepper flakes as desired. Gently stir to combine. Taste & adjust seasoning as desired. Set aside to marinate about 30 minutes or transfer to an airtight container & store in the refrigerator for up to 2 days.
Add the ricotta cheese to a food processor with the remaining 2 Tbsp extra virgin olive oil. Season with a good pinch of kosher salt. Let the processor run until the ricotta is whipped with a light & creamy texture – this takes a full 2-3 minutes so be patient & stop to scrape down the sides of the food processor as needed. Taste & adjust seasoning as desired. Set aside for serving.