In a large Dutch oven or heavy pot, heat the oil over medium-high heat. Add the onions and celery and cook until golden, stirring occasionally, takes about 6 to 8 minutes.
Stir in the garlic, thyme, and rosemary and cook until fragrant, about 2 minutes. Season to taste with salt and pepper.
Add the carrots, potatoes, and stock to the Dutch oven. Bring to a boil then reduce to a simmer. Cook, stirring occasionally until the potatoes are very soft and start falling apart, 45 minutes to 1 hour.
Remove the thyme and rosemary sprigs. Taste and season with additional salt and pepper, if needed. Serve hot.