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