Heat a large sauté pan over medium-high heat with the EVOO and butter. Add the onions and cook until caramelized, 5-6 minutes.
Add the sliced Brussels sprouts, allspice, sage, some salt and freshly ground pepper, and toss to combine. Add the stock, bring up to a bubble, then reduce the heat and simmer until the Brussels sprouts are tender, about 15 minutes. In the last three minutes of cooking, stir in the radicchio.