1. Put milk into a shallow dish. Add anchovy fillets; soak 10 minutes. Drain on paper towels, and pat dry. Cut fillets to be the same length as the sage leaves. Lay each sage leaf face up on a large cutting board. Place an anchovy fillet on half of the sage leaves; crush with fork tines, being careful not to tear leaves. Sandwich with another leaf, face down. Press with the back of a spoon to seal.

2. Preheat oven to 200 degrees. Put flour into 1 bowl and egg into another. Heat 1/4 inch oil in a medium skillet over medium-high heat. Coat 6 of the anchovy-sage sandwiches with flour, shaking off any excess, then with egg, allowing excess to drip off. Fry, turning once, until golden, 45 seconds to 1 minute per side. Drain on paper towels. Transfer to oven to keep warm. Repeat with remaining anchovies in batches. Serve immediately.