Crunchy Fried Eggs on a Dandelion Salad

INGREDIENTS

• 6 tablespoons peanut oil, plus more for frying
• 2 tablespoons white-wine vinegar
• Coarse salt and freshly ground pepper
• 1 large white onion, peeled and very thinly sliced crosswise
• 1/3 cup milk
• 1/3 cup all-purpose flour, for dredging
• Pinch of paprika
• 4 large eggs
• 14 ounces very tender yellow or green dandelion leaves, trimmed, rinsed, and chilled
• 1 tablespoon finely chopped shallots