In a large skillet, heat the olive oil over medium heat. Add the chicken pieces and cook until they’re no longer pink and fully cooked, about 5 to 7 minutes. Transfer the chicken to a plate and keep warm.
Using the same skillet, cook the chopped onions until they’re soft and translucent, which should take about 3 to 5 minutes. Add the minced garlic and cook for another 30 seconds until fragrant. Season with salt and pepper.
Gradually whisk in the milk and dried mustard, and cook until the mixture starts to thicken. Stir in the mozzarella and cheddar cheeses until they melt and the sauce is smooth.