When shopping for endive, choose those that feel heavy in your hand and have tightly compacted heads.
Preheat the oven to 350°. Butter a large 9x13-inch baking dish or gratin pan.
Trim any brown areas from the base of each endive and remove any less-than-perfect leaves. Cut each endive in half lengthwise. Heat 1 tablespoon each butter and olive oil in a large skillet over medium-high heat. When hot, add as many endive as will fit without crowding, cut side down, and cook until speckled brown, about 4 minutes. Turn with tongs to briefly brown the other side, another 4 minutes. Transfer to the buttered dish, cut side up, and continue with the remaining endive, adding more butter and oil as needed. The browned endive should fit snugly into a single layer in the baking dish. Season with sugar, salt, and pepper. Add chicken stock, cover tightly with foil, and braise until tender, about 35 minutes.