Melt Unsalted Butter (2 tablespoon) in a large heavy pot over medium heat. Add Fresh Thyme (2 sprig), Onion (1) and Garlic (2 clove). Season with Kosher Salt and Freshly Ground Black Pepper (to taste). Cook until onion is completely soft and translucent, 10-12 minutes.
Increase heat to medium-high; add Tomato Paste (2 tablespoon). Continue cooking, stirring often, until paste has begun to caramelize in spots, 5-6 minutes—it will begin to stick to the bottom of the pan.
Add Canned Whole Peeled Tomatoes (28 ounce) with juices and Water (4 cup) to pot. Increase heat to high; bring to a simmer. As the plum tomatoes rise to the surface while the soup simmers, use scissors to cut them up.
Reduce heat to medium. Simmer until flavors meld and the soup has reduced by a quarter, 45 minutes or so. Remove soup from heat; discard thyme sprigs. Working in small batches, purée soup in a blender until smooth or purée with an immersion blender.
Stir in Heavy Cream (1/4 cup). Taste and adjust as needed. I like adding Granulated Sugar (1 teaspoon) and I add at least a teaspoon of Kosher Salt and Freshly Ground Black Pepper (to taste). Simmer soup until flavors meld, 5-10 minutes longer. Taste again, and add more cream, if desired.
Ladle soup into bowls and put Parmigiano-Reggiano (to taste) over top. Serve with more pepper on the side and Bread (to taste).