Preheat the grill to high heat.
Heat the olive oil in a small saucepan until hot. Add the sage and allow the sage to infuse its flavor into the oil. Remove from the heat when the sage becomes fragrant and slightly crispy, a few minutes.
Grill the endive and radicchio until slightly wilted with good grill marks, about 4 minutes per side. Turn the endive and radicchio cut-side up and top with the gorgonzola. Close the lid and grill until the cheese has softened, 2 minutes.
Remove the endive and radicchio to a platter. Drizzle the infused olive oil over the top. Serve immediately.