Dip the squash blossoms in cold water and drain them thoroughly on paper towels. Remove the stamens from the male blossoms. In a small bowl, mix all filling ingredients with a whisk or an electric mixer until smooth. Fill each squash blossom with 2 teaspoons of filling.
To make the batter, in a medium bowl, stir together the flour, water, milk, egg and salt. Let sit for one hour. Fill a heavy saucepan or skillet with oil to a depth of 2 inches. Heat over medium heat to 375 degrees. Dip a few squash blossoms into batter, covering entire blossom, and drop into the hot oil. Fry until golden brown, about 1 minute, turn over and fry on the other side. Remove with a slotted spoon and drain on paper towels. Repeat with the remaining blossoms, being careful not to overcrowd the pan. Add salt and pepper and serve immediately.