Spring Vegetable Risotto with Poached Eggs

INGREDIENTS

• 2 cups shelled fresh (or frozen, thawed) fava beans or peas (from about 2 pounds pods)
• Kosher salt
• 1 tablespoon distilled white vinegar
• 6 large eggs
• 8 cups low-sodium chicken broth
• 2 tablespoons unsalted butter, divided
• 1/4 pound chanterelles or crimini (baby bella) mushrooms, halved or quartered if large
• 2 tablespoons olive oil
• 2 large leeks, whites and pale greens only, chopped
• 1 fennel bulb, chopped
• 4 garlic cloves, finely chopped
• 2 cups arborio rice
• 1 cup dry white wine
• 1 bunch flat-leaf spinach, trimmed, leaves torn
• 2 tablespoons crème fraîche or sour cream
• 1 1/2 cups finely grated Pecorino or Parmesan (about 3 ounces) plus more for shaving
• 1/4 cup chopped fresh chives plus more for serving
• Freshly ground black pepper