Whisk together the eggs and buttermilk, in a large bowl. In a separate bowl, whisk together the cornmeal, flour, baking soda, salt, and sugar. Add the wet ingredients to the dry ingredients, then add the onion and jalapenos and stir until incorporated and the batter is thick.
In a heavy-bottomed pot (Dutch oven) or deep fryer, heat enough oil to come halfway up the sides of the pot, to 360 degrees F.
Working in batches, drop the batter, 1 tablespoon (I use a cookie dough scoop) at a time, into the oil, being careful to not overcrowd the pot. Fry until deep golden on all sides, turning in the oil for even cooking, about 5 minutes. Transfer the hush puppies to a paper towel-lined dish and sprinkle with salt (if desired) while hot.
This recipe yields about 12 to 15 pieces, depending on the scoop size.