Preheat the oven to 375 degrees.
Put the sundried tomatoes in a heatproof bowl and cover with 4 cups of boiling water.
Drain the canned tomatoes and preserve the liquid. Cut them in 1/2 and put in a shallow roasting pan. My oven is only big enough for an 8x8 pan and it works for this as well. Try to drain the tomato juice from the roasting pan after you've finished putting them in there, and keep the liquid. Draining will help them roast better.
Drizzle with two tablespoons of olive oil and sprinkle with thyme.
Roast in the oven for about 30 minutes. If you used a more shallow pan, the tomatoes will be drier and browned. In the 8x8 it just gives them a nice flavor. You can roast them for longer if you want them to be drier.
Once the tomatoes are done roasting, pour the soaking liquid from the sundried tomatoes into the roasting pan. It sounds gross, but it's totally good. Trust me. Roughly chop the sundried tomatoes too and add those to the roasting pan also. Break up the roasted tomatoes and scrape up the browned bits at the bottomg at the same time while mixing all of this together.
Heat the remaining olive oil in a soup pot over medium to medium-high heat (whatever is appropriate for your cookwear). When hot, add the garlic and cook until it begins to change color - about 1 minute. Add the carrot and onion and cook until they start to sweat - about 3 minutes. Sprinkle with salt and pepper, then add the honey and stir until it melts.
Add the reserved liquid from the canned tomatoes and stir for a few minutes - until the liquid begins to darken. Add the stock and the contents of the roasting pan (at this point, it's the whole peeled tomatoes, the sundried tomatoes, and the soaking liquid for the sundried tomatoes). Chop the basil and add it to the soup.
Turn the heat up and bring the soup to a boil and the lower so it boils gently. Cover and cook for 30 minutes. (It can cook for longer too, but only needs about 30 minutes. I think it tastes a bit better when it cooks for about an hour).
Turn off the heat and let it the soup stop boiling and cool a bit. Use an immersion blender to puree the soup. (Or you can let the soup cool to room temperature and puree it in a blender and return to the pan and reheat). Stir in heavy cream and serve or make ahead and reheat when you're ready. This stores will in the refrigerator - I haven't tried in the freezer.