Preheat oven to 400F. Bring a large pot of salted water to boil.
Add pasta and cook until just tender, about 8 minutes.
Drain and set aside.
Melt 3 Tbsp. butter in a large ovenproof skillet over medium heat.
Whisk in flour, mustard and 1/2 tsp. salt until smooth. Slowly whisk in milk and half-and-half and bring just to a simmer. Stir in cheese, a little at a time, until melted.
Remove pan from heat and stir in peas, ham and pasta. Stir to coat with sauce.
Sprinkle cracker crumbs over top of pasta and dot with remaining 1 Tbsp. butter.