Cheesy Broccoli Chicken Noodle Casserole

Ingredients
12 ounces wide egg noodles
2 tablespoons unsalted butter
1 medium yellow onion, chopped
2 cloves garlic, minced
2 cups cooked chicken, shredded or diced
16 ounces frozen broccoli florets, thawed and drained
10.5 ounces (1 can) condensed cream of chicken soup
10.5 ounces (1 can) condensed cream of mushroom soup
1 cup milk (whole or 2%)
1 cup sour cream or plain Greek yogurt
1 teaspoon dried Italian seasoning
1/2 teaspoon black pepper
1/4 teaspoon salt (or to taste, depending on soup sodium)
2 cups shredded sharp cheddar cheese, divided
1/2 cup shredded Monterey Jack cheese (optional, for extra meltiness)

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