Bring a large pot of salted water to a boil. Add 1 lb fusili or rotini and cook according to package directions until al dente. Reserve some pasta cooking water (optional), then drain and set the pasta aside.
While the pasta cooks, heat olive oil in a large skillet over medium-high heat. Add the 2–3 boneless, skinless chicken breasts cut into 1-inch pieces. Sprinkle the chicken with 1 TB fresh thyme, salt, and pepper to taste.
Cook the chicken, stirring occasionally, until browned and cooked through. Transfer the cooked chicken to a plate and set aside.
Reduce the heat to medium. In the same skillet, add 2 TB butter and melt.
Add 2 TB all-purpose flour to the melted butter and whisk continuously to form a roux. Cook until the raw flour smell is gone (about 1–2 minutes).
Stir in 2 tsp minced garlic and cook briefly until fragrant (about 30 seconds).
Gradually whisk in 2 c milk until smooth. Bring the mixture to a gentle simmer and cook, whisking frequently, until the sauce thickens and coats the back of a spoon.
Remove the skillet from the heat and stir in 1 c shredded triple cheddar cheese until fully melted and the sauce is smooth. Taste and adjust salt and pepper if needed.
Return the cooked chicken and the drained pasta to the skillet. Toss to combine, adding a little of the reserved pasta water if the sauce needs loosening.
Sprinkle 2 TB fresh thyme and 1 TB oregano over the pasta and toss to distribute evenly.
Transfer to bowls or a serving dish and top with 1/4 c grated Parmesan cheese. Serve warm.