In a large pot, heat a drizzle of olive oil over medium heat. Add the diced onion, carrots, and celery. Sauté for about 5 minutes, or until the vegetables begin to soften.

Stir in the minced garlic, dried thyme, and dried rosemary. Cook for an additional minute until fragrant.

Add the diced potatoes and chicken broth to the pot. Bring to a boil, then reduce heat and let simmer for about 15 minutes, or until the potatoes are tender.

Stir in the potato gnocchi and cook according to package instructions, usually about 2-3 minutes.

Reduce the heat to low and slowly stir in the heavy cream and shredded cheddar cheese until melted and well combined. Season with salt and pepper to taste.

Serve hot, garnished with chopped green onions or chives.