Place one graham-cracker rectangle on a tray. Add one chocolate piece and one standard-size marshmallow, then top with a second graham-cracker rectangle to make a sandwich; repeat to form 8 s'mores.

Chill the assembled s'mores for at least 30 minutes, or freeze them for 20-30 minutes, until firm. This cold, firm center helps the sandwiches stay together while the batter sets in the hot oil.

Whisk the flour, granulated sugar, baking powder, and fine salt in one bowl. In a separate bowl, whisk together the egg, milk, and vanilla extract.

Add the wet ingredients to the dry ingredients and stir just until combined. The batter should be thick enough to coat each s'more; if it seems too thick, stir in a small amount of the additional milk.

Pour the neutral oil into a deep, heavy pot, making sure the pot is no more than half full. Heat the oil to 350°F/175°C, checking the temperature with a suitable thermometer before frying.

Dip each chilled s'more completely in the batter, turning carefully so every side is covered. Allow excess batter to drip back into the bowl before transferring the coated sandwich to the oil.

Carefully lower only a few coated s'mores into the hot oil at a time so the temperature remains steady. Fry for approximately 1-1 1/2 minutes per side, turning once, until the coating is puffed and golden brown.

Remove the fried s'mores with a slotted spoon and place them on a wire rack or paper towels to drain. Dust with confectioners' sugar and serve while warm, taking care with the molten chocolate and marshmallow center.