Fire up a charcoal grill or heat a cast-iron grill panover medium-high heat.
In a small nonreactive bowl, combine the oil, vinegar, 2 tablespoons of the bacon drippings, the brown sugar, mustard, salt, and pepper. Whisk until an emulsion is formed and set the vinaigrette aside at room temperature.
Coat the quartered radicchio in the remaining tablespoon bacon drippings. Put the radicchio onto the hot grill or grill pan and cook until the edges are slightly wilted, about 2 minutes per side.
Transfer to a plate and cover with a stainless-steel bowl; let the radicchio steam for 5 minutes.
Drizzle the vinaigrette over the radicchio wedges and serve immediately.