Melt 1 tablespoon of butter in a small saucepan over medium heat.

Add 2 tablespoons of flour to the melted butter and cook for 2 minutes, stirring constantly, to create a roux.

Gradually whisk in the hot milk, stirring continuously to prevent lumps, until a smooth white sauce forms. Set aside.

In another saucepan, melt 3 tablespoons of butter over low heat.

Add crushed garlic, Italian seasoning, red pepper flakes, and black pepper to the melted butter.

Cook the garlic and spices for 2 minutes on low heat, stirring constantly, to infuse the butter with flavor.

Pour in the white cooking wine and chicken broth, stirring until all ingredients are well combined.

Simmer the sauce for 20 to 30 minutes, allowing it to reduce and thicken slightly. Set aside.

Slice the chicken breasts into thin strips.

Place the chicken strips in a small bowl with flour, salt, and pepper. Toss to coat each piece thoroughly.

Heat olive oil in a large skillet over medium-high heat.

Saute the floured chicken strips in the hot olive oil until almost fully cooked.

Add the thinly sliced bell peppers and red onion to the skillet with the chicken.

Continue to saute until the chicken is fully cooked and the vegetables are crisp-tender.

Combine the white sauce and scampi sauce in the skillet, stirring until well combined and heated through.

Pour the sauce over the chicken and vegetable mixture, and heat through.

Serve the chicken scampi over cooked and drained angel hair pasta.