Put the dried tomatoes in a heatproof bowl and cover with 2 cups boiling water.
Drain the canned tomatoes and reserve the liquid; halve them and put in a shallow roasting pan; drizzle with 2 tablespoons of olive oil and sprinkle with the thyme.
Roast, turning once or twice, until the tomatoes are dried and lightly browned, about 30 minutes.
When the tomatoes are done, drain the dried tomatoes and pour their soaking liquid into the roasting pan.
Use a wooden spoon to scrape up all the browned bits from the bottom of the pan, breaking up the roasted tomatoes at the same time.
Roughly chop the dried tomatoes and add them to the roasting pan.
Put the remaining olive oil in a deep skillet or medium saucepan over med-high heat.
When hot, add the garlic and cook just until it begins to color, a minute or so.
Add the carrot and onion and cook until they start to release their liquid, about 3 minutes.
Sprinkle with salt and pepper, then add the honey and stir until it melts, just a few seconds.
Add the reserved liquid from the canned tomatoes and continue stirring until the liquid dries out and darkens, about 5 minutes.
Stir in the stock, along with the contents of the roasting pan.
Turn the heat to high and bring the soup to a boil, then decrease heat so it bubbles gently.
Cover and cook until the vegetables are very tender, about 30 minutes.
Garnish with the parsley and serve.
*Wintertime Tomato and Rice Soup--add 1 cup short-grain rice, like Arborio, to the pan just after the reserved canned tomato liquid has cooked; increase the stock to 6 cups.
*Elegant Wintertime Tomato Soup--use an immersion blender to puree the finished soup in the pan; or cool the soup to room temperature, carefully puree in a blender, and return to the pan to reheat; stir in 1 cup heavy cream, sour cream, or any milk and heat gently.