In a medium stainless steel skillet, heat 1 tablespoon (15 ml) olive oil over medium heat until shimmering. Add shallots and ½ teaspoon kosher salt. Cook, stirring occasionally, until golden brown and jammy, about 15 minutes, adding 2 tablespoons of water at a time if shallots start to stick to the bottom of the skillet. Remove from heat, and transfer half of shallot mixture to a large bowl. Let cool completely, about 15 minutes.
Meanwhile, off heat, add sherry vinegar and thyme to remaining shallots in skillet; stir to combine and set aside.
In a food processor, process ricotta, Parmigiano-Reggiano, lemon zest, garlic, black pepper, remaining 3 tablespoons (45 ml) olive oil, and remaining 1 teaspoon salt in a food processor until smooth and creamy, about 1 minute, stopping to scrape down sides of bowl as needed.
Transfer ricotta mixture to the large bowl containing shallots, and gently fold until just combined.
Spoon whipped ricotta mixture into a shallow bowl. Using the back of a spoon, create swirls and ridges on the surface of ricotta dip. Top with shallot-sherry mixture. Drizzle with additional olive oil, and sprinkle with flaky sea salt and thyme leaves. Serve with crudités, bread, and/or crackers.
