Melt butter in a large heavy pot over medium heat. Add thyme, onion, chipotle, jalapeno, and garlic. Cook until onion is completely soft and translucent, 10–12 minutes. Increase heat to medium-high; add tomato paste. Continue cooking, stirring often, 5–6 minutes.
Add tomatoes with juices, 1 tsp. sugar, 2 cups of water, and 3 cups chicken broth to pot. Increase heat to high; bring to a simmer. Reduce heat to medium. Simmer until flavors meld, 45–55 minutes. Remove soup from heat; let cool slightly. Working in small batches, purée soup in a blender until smooth. Return to pot. Rewarm before continuing.
Stir in 1/4 cup half-n-half. Simmer soup until flavors meld, 10–15 minutes longer. Add more cream, if desired.
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