Pour the curdled milk into the cheesecloth and let it drain for 45 minutes to 2 hours. The longer you let it rest, the thicker the ricotta will be.
Preheat the oven to 250° degrees Fahrenheit. While the ricotta is draining, slice the cherry tomatoes in half and place them on a baking sheet lined with parchment paper. Generously drizzle the tomatoes with good olive oil, and then sprinkle with salt, pepper, and sprigs of thyme. Mix them with your hands so everything is evenly coated, and then arrange them cut-side up.