1. Preheat the oven to 375°F. Butter a 2-quart gratin dish and coat the sides with Parmesan cheese.
2. Boil the Brussels Sprouts in salted water for 5 minutes, then drain. Rinse in cold water to stop cooking, then dry as well as possible. Coarsely chop, leaving plenty of large chunks.
3. In a separate bowl, whisk the flour, Ranch seasoning mix, half-and-half and eggs. Add the Brussels sprouts and onions and stir to coat, then transfer everything to the gratin dish.
4. Bake for 25 minutes, then remove and scatter breadcrumbs that have been mixed with the melted butter over the top. Continue to bake another 20 minutes, until browned and crisp on top. If the breadcrumbs aren’t as browned as you’d like them to be, place under broiler to finish for 1-2 minutes. Let rest for at least 10-15 minutes before serving.
For safe meat preparation, reference the USDA website.