Cook the carrots in a pot of boiling salted water until crisp-tender, about 4 minutes. Drain.
Heat the oil in large pot over medium-high heat. Add the garlic, tarragon, and thyme; sauté about 30 seconds. Add the carrots and remaining vegetables; sauté until just tender, tossing often, about 6 minutes. Sprinkle with salt and pepper. Add butter and stir to melt and blend in. Serve.
Notes
Make ahead tip: Blanch carrots and cut up other vegetables a day ahead and chill them in a plastic bag overnight.