Bring a large pot of salted water to a boil over high heat. Cook the noodles according to the package directions for about 11 minutes. Drain and run cold water over the noodles. Set aside.
While the noodles are cooking, make the sauce. Add the mayonnaise, mustard, vinegar, olive oil, salt, tarragon, dill, and paprika to a bowl. Mix until well combined. Set aside.
Add the cooled noodles, ham, peas, onions, cheddar, and sauce to a bowl. Stir to combine.
This can be served immediately. However, the longer it sits, the more the flavors will develop.