In a large bowl, mix the cornmeal, onions, jalapeno and a pinch of salt. Add enough of the buttermilk to make a stiff batter. You may not need the whole 2 cups.
Heat the peanut oil in a deep fryer or a large heavy bottomed pot to 250 degrees F.
Drop the batter into the hot oil by teaspoonfuls. The hushpuppies will turn over in the oil as they cook. They are done when they are brown all over, 6 to 8 minutes. Remove them from the oil with a slotted spoon, drain on paper towels and season with salt. Keep the hushpuppies warm while you fry the remaining batter. Serve hot.
Cook's Note: If you can't find self-rising cornmeal, substitute 2 cups cornmeal plus 3 teaspoons baking powder and 1/4 teaspoon salt.