Trim any fat from the chicken and cut into 1‑inch cubes.
Heat the olive oil in a large skillet over medium heat. Add the chicken and diced onion and cook, stirring occasionally, until the chicken is cooked through and the onion is softened, about 6–8 minutes.
Add the minced garlic during the last minute of cooking and cook until fragrant, about 1 minute. Remove the chicken mixture from the skillet and set aside.
Over low heat, pour 1 cup of the milk into the hot skillet. Whisk in the flour until smooth to make a roux.
Slowly whisk in the remaining 1 cup milk and the chicken broth, keeping the sauce smooth.
Add the salt and black pepper and bring the mixture to a boil over medium heat, whisking frequently, and allow it to thicken slightly.
Stir in the can of mild Rotel and the uncooked angel hair pasta. Increase heat to high to bring the mixture back to a boil, then reduce heat to medium‑low, cover, and cook 8–10 minutes, stirring occasionally, until pasta is al dente.
Cut the cream cheese into pieces and stir into the pasta along with the shredded Mexican cheese until melted and smooth.
Add the cooked chicken back to the skillet and heat through, stirring to combine.
Serve hot, garnished with the diced tomato if desired.
