Heat oven to 250°F. Spread fresh tomatoes, garlic, and 2 sprigs thyme on a rimmed baking sheet and toss with ¼ cup olive oil and ¼ teaspoon salt. Roast for 4 hours, or until tomatoes have collapsed and browned in spots, then set aside to cool. Once cool, squeeze garlic cloves out of their skins and discard skins, along with the thyme. Return garlic to the tomato mixture and scrape into a bowl or lidded container. (You can do this step up to 3 days ahead of time—just refrigerate the mixture if you’ve made it in advance.)

Heat remaining oil in a medium, heavy-bottom pot over medium heat. When oil is warm, add onions and cook, stirring, for 3 to 4 minutes, until they begin to soften. Add fennel and continue to cook, stirring, for another 5 to 7 minutes.

Add canned tomatoes and their juices, stir to combine, and add water. Bring mixture to a simmer over medium-high heat. Add remaining thyme, parmesan rinds, the roasted tomato mixture, and remaining salt. Reduce heat to medium-low and simmer for 35 to 40 minutes.

Discard thyme and parmesan rinds and puree soup with an immersion blender (or standing blender). Strain through a fine-mesh sieve, return soup to the pot, taste and adjust seasoning as needed, and keep warm until ready to serve. Soup will keep in the refrigerator for about 1 week, or in the freezer for up to 2 months.