In a small skillet, melt the butter over medium heat. When the butter foams, add the uncooked pasta and cook, stirring often, until toasted and golden, about 3 minutes.
Meanwhile, in a Dutch oven, heat the olive oil, two turns of the pan, over medium to medium-high heat. Add the onion, celery, carrots and garlic, and season with salt and pepper. Cover and cook, stirring occasionally, until the vegetables are tender, 6-7 minutes.