Instructions
Step 1
Heat a charcoal grill or set a gas grill to medium-high. In a small bowl, whisk together 2 tablespoons of the oil and the sherry vinegar. Set aside.
Step 2
In a small skillet over medium heat, melt the butter. When the foam subsides, add the garlic and shallot and cook, stirring occasionally, until softened, 3–4 minutes. Add the chives and cook for about 1 minute more. Season to taste with black pepper and remove from the heat.
Step 3
Thread the morels onto skewers. When the grill is preheated, use tongs and a wad of oiled paper towels to grease the grates. Add the morels and grill, turning occasionally, until slightly charred and just cooked through, about 10 minutes. Transfer to a cutting board, remove the skewers, then coarsely chop the mushrooms. Add them to the butter mixture and toss to coat.
Step 4
Drizzle the remaining oil over both sides of the bread slices, then grill, turning once, until there are grill marks on both sides, about 4 minutes total. Turn off the heat. Top the slices evenly with the fontina, cover, and grill until the cheese is melted, 30–60 seconds more. Transfer the toasts to a plate, top with the buttered morels, and drizzle with the vinaigrette. Season to taste with flaky salt and serve hot.