Preheat the oven to 375F and butter a large gratin dish.
Sauté the onion in the olive oil for five minutes in a medium saucepan set over medium heat. Sprinkle the flour over the onions and continue sautéing the mixture for 30 seconds. Add the salt, pepper, rubbed sage, and milk to the pan and stir constantly for 3 to 5 minutes until the sauce thickens.
Stir broccoli and cheese into the sauce, bring the mixture to just a simmer, and then turn it out into the buttered gratin dish. Stir together the melted butter, bread crumbs, and 1/4 cup Parmesan cheese, and sprinkle the bread crumbs over the gratin. Bake the broccoli gratin in the preheated oven for 15 to 20 minutes, until it is hot and bubbly, and the bread crumbs have turned golden brown.