Spring Vegetable Risotto with Poached Eggs

INGREDIENTS

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