Mix flour, eggs, butter, sugar, egg yolk, lemon zest, rum extract, and salt together in a large bowl to create a soft dough. Cover with plastic wrap; let stand for 30 minutes.
Roll dough into a thin log the width of your pinky finger, about 1/4 inch. Cut log into small pieces; roll into balls. Dust with flour to prevent from sticking.
Heat oil in a deep-fryer or large saucepan. Place a few balls of dough in a sieve to shake off excess flour. Cook in the hot oil until golden brown, about 2 minutes. Transfer to a paper towel-lined plate using a slotted spoon. Repeat with remaining balls of dough.
Pour honey into a saucepan over low heat. Cook until a small amount of honey dropped into cold water forms a soft ball. Add fried balls of dough to the hot honey; stir gently with a wooden spoon until coated.
Rinse a serving plate and shake off the water. Pile dough balls onto the serving plate in the shape of a dome or ring using damp hands or a damp wooden spoon. Garnish with sugar sprinkles. Let cool completely.