Wash and dry all produce. Bring a large pot of salted water to a boil. Halve, peel, and dice onion. Peel and finely dice carrot. Mince or grate garlic. Strip thyme leaves from sprigs. Core, seed, and thinly slice poblano.

Heat a drizzle of olive oil in a large pan over medium heat. Add beef and season with salt and pepper. Break up meat into pieces with a spatula or wooden spoon. Cook until browned and lightly crisped at edges, 5-6 minutes. Remove from pan and set aside.

Add poblano to same pan over medium-high heat. Toss until slightly blistered, 3-4 minutes. Add garlic and cook until fragrant, about 30 seconds. Season with salt and pepper. Set aside with ground beef.

Heat another drizzle of olive oil in same pan over medium heat. Add onion, carrot, and thyme, then season with salt and pepper. Cook until softened, about 5 minutes, stirring occasionally. Add beef, poblanos, and diced tomatoes. Bring to a simmer and let bubble 5 minutes. Season with salt and pepper.

Meanwhile, add linguine to boiling water. Cook until al dente, 9-11 minutes. Drain, reserving 1/2 cup pasta water.

Add pasta to pan with sauce along with a splash of pasta water. Add the sour cream. Toss to combine, then season with salt and pepper. Serve pasta with a sprinkle of Parmesan on top.