Bring a large pot of salted water to boil.

Wash lemon and orange; zest half of each fruit, avoiding white pith. Finely chop zests together with parsley; place in a bowl and stir in Parmigiano-Reggiano. Set gremolata aside.

In a medium saucepan, bring milk just to boil over medium-low heat; remove from heat. In a large saucepan, melt butter over low heat. Add flour; cook, stirring constantly with a wooden spoon for 2 minutes. Do not brown. Remove from heat. Add 2 tablespoons milk to flour mixture, stirring constantly until milk is incorporated. Repeat until ½ cup of the milk has been added. Add remaining milk ½ cup at a time, incorporating between additions, until all milk has been added. Return to low heat and cook, stirring frequently, especially along corners of pan, until sauce is the consistency of thick cream. Stir in remaining cheeses; cover to keep warm.

Cook pasta in boiling water until al dente. Drain and immediately transfer to a large serving bowl. Add cheese sauce, toss to combine and divide among bowls. Sprinkle with gremolata and serve immediately.