Make the syrup: Combine 1 cup water, the jelly and 2 tablespoons of the elderflower liqueur in a small saucepan over medium heat; bring to a boil, then reduce the heat to low and simmer until syrupy, 20 to 25 minutes. Transfer to a medium heatproof bowl and let cool, stirring occasionally.
Meanwhile, make the doughnuts: Whisk the flour, sugar, baking powder, salt and nutmeg in a large bowl. Stir in the cream, eggs, vanilla and the remaining 3 tablespoons elderflower liqueur until smooth.
Heat about 1 1/2 inches vegetable oil in a large pot over medium heat until a deep-fry thermometer registers 350 degrees F. Working in batches, drop heaping tablespoonfuls of the batter into the oil and fry, turning, until golden, 4 minutes. (Reduce the heat if the doughnuts are browning too quickly.) Remove with a slotted spoon and drain on paper towels, then roll in cinnamon sugar. Serve with the strawberry syrup.