Begin by making the simple syrup and add sugar, water and vanilla bean to a small pot.
Bring mixture to a boil and then reduce to a simmer until it thickens slightly and turns into a light amber color syrup, about 15 minutes.
Once done, remove vanilla bean and discard and remove syrup from heat and let cool while you make the bimuelos.
For the bimuelos, break up the matzo into small pieces and soak in a large bowl of warm water for a few minutes.
Meanwhile, heat a large deep skillet with about ¼ in of oil over medium heat.
Once the matzo is soaked, squeeze all the water out with your hands very well and add the whisked eggs, salt and pepper and give everything a good mix.
Spoon 2 tablespoons worth of mixture and carefully drop in hot oil. The bimuelos should immediately sizzle if it's hot enough. (You can also test this with a small piece of batter beforehand).
Fry bimuelos in oil until first side is lightly golden brown, about 3-4 minutes. Carefully flip over and cook other side for another 2-3 minutes until both sides are golden brown.
Once bimuelos are done frying, drain on reserved paper-towel lined plates and immediately grate Parmigiano Reggiano cheese while still hot.
Serve bimuelos alongside simple syrup to dip into.
Notes
Make the simple syrup ahead of time to make the recipe even quicker.