Bring a large pot of lightly salted water to a boil. Add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes.

Preheat the oven to 375 degrees F (190 degrees C).

Meanwhile, melt butter in a saucepan over medium heat and cook garlic for 1 minute. Whisk in flour until a paste forms. Pour in milk and cream, whisking continuously until smooth. Stir in 3/4 of the Parmigiano-Reggiano cheese and nutmeg. Add drained penne pasta and cooked chicken; stir to combine. Pour mixture into a casserole dish. Sprinkle with remaining cheese.

Bake in the preheated oven until cheese is melted, 10 to 12 minutes.