Butter metal 9-by-13-inch pan. Brown sausage and onion in skillet over medium 10 minutes, breaking up meat, to 160°F. Drain; cool 15 minutes.
Whisk eggs, milk, mustard, salt, and pepper. Put rye, sausage mixture, and Gouda in pan; pour custard over and press bread down.
Cover; refrigerate 8 to 12 hours, additional to listed prep and cook times.
Heat oven to 350°F. Uncover pan; loosely foil-tent and bake straight from refrigerator 30 minutes.
Uncover; bake 20 to 25 minutes more until puffed and center 160°F. Rest 10 minutes before slicing.