Heat grill to high (450°F to 550°F) with an area cleared of coals (for charcoal grill) or a burner turned off (for gas) to make an indirect-heat area. Stir together butter, anchovies, reserved anchovy oil, tarragon, mint, parsley, chives, lemon juice, and pepper in a bowl. Let stand next to the grill to warm, whisking occasionally, until butter begins to break down but not melt.
Place carrots, endive, and onions on a rimmed baking sheet. Drizzle with olive oil, and toss to coat. Remove vegetables from baking sheet, and place on cooking grate over direct heat. Grill, uncovered, turning occasionally, until lightly charred, 6 to 7 minutes. As vegetables char, transfer them to indirect heat. Continue to grill, covered, until vegetables are tender but not mushy: endive, about 2 more minutes; carrots, about 8 more minutes; and onions, about 10 more minutes. Remove vegetables to a platter. Cool 15 minutes. Dollop with butter mixture.