Mix the eggs and sugar until they are pale yellow and fluffy, about 5 minutes. You can use a standing mixer with a whisk attachment or a hand mixer.
Add the melted and cooled butter and the vanilla extract. Mix until evenly combined.
Add the flour and salt and mix just until the flour is incorporated. Use a rubber spatula to to scrape down the sides and bottom of the bowl, to make sure that the flour is all incorporated and the batter is evenly mixed.
Heat up the pizzelle baker.
Using a portion scoop or two spoons, place about 1 1/2 Tablespoons of batter slightly behind the center of each pizzelle design. The batter will spread forward as it bakes. Bake for a few minutes, just until the pizzelles are slightly golden.
You can also place the batter in a large pastry bag and pipe out the batter onto the pizzelle iron that way.
If the 2 pizzelles fuse together as the batter spreads and they are baking, use a butter knife to gently separate them.
As soon as you take the Trubochki off the pizzelle baker, immediately wrap the hot Trubochki around a clean marker. You won't be able to shape them into a cylinder if they cool even a little bit, so work really fast. You don't need to use a marker; you can use anything that will create a cylinder out of the Trubochki, but markers are really convenient and create the perfect opening for the filling.
Repeat with all the batter. I usually get about 32 Trubochki.
You can make the Trubochki up to 5 days in advance. Store them at room temperature, in a loosely covered box, baking pan or container, so that they stay crisp. If you cover them with plastic wrap, they will soften.