Heat 2 teaspoons of olive oil in a large pot over low heat. Cook and stir sliced garlic until tender but not browned, for about 3 minutes.

Pour in the canned tomatoes with juice and mash them with a potato masher, leaving chunks. Stir in tomato paste, red wine, sugar, oregano, basil, salt, and black pepper. Mix until tomato paste smoothly combines. Bring to a simmer and cook while preparing vegetables.

Heat 1 tablespoon of olive oil in a skillet over medium heat. Cook and stir chopped carrot and celery until tender, for about 5-8 minutes. Stir these into the sauce.

In the same skillet, cook and stir green peppers and onions until onions turn translucent, for another 5-8 minutes. Mix these into the sauce.

Heat another tablespoon of olive oil in the skillet and cook sliced mushrooms until they release their liquid, for about 10 minutes. Add mushrooms to the sauce.

Allow the sauce to simmer while cooking the chicken.

Prepare chicken: beat eggs in a bowl. Place flour in another bowl. Heat ¼ cup olive oil in a skillet over medium heat. Dip chicken pieces into the egg, then dredge in flour. Brown chicken on both sides, for about 15 minutes. Set chicken aside.

Preheat oven to 325°F (165°C).

Spoon 1 cup of the tomato sauce into the bottom of a large Dutch oven. Layer chicken pieces over the sauce and pour the remaining sauce and vegetables on top. Cover the Dutch oven.

Bake in preheated oven until chicken is tender and no longer pink inside, for about 1 hour.

If the sauce begins boiling harder than a simmer, reduce oven heat to 300°F (150°C).

About 15 minutes before serving, bring a large pot of salted water to a boil. Add linguine pasta. Cook pasta until tender but firm, for about 10-12 minutes. Drain.