Begin by peeling the large yellow onion. Cut it in half from top to bottom, then place the flat side down on the cutting board. Slice the onion into thin half-moons, about 1/4 inch thick.
Turn on your griddle to medium heat. Allow it to preheat for a few minutes. You can test if it's ready by sprinkling a few drops of water onto the surface; if they sizzle and evaporate quickly, it's time to start cooking.
Once the griddle is hot, drizzle 1 tablespoon of olive oil evenly across the surface. Add 1 tablespoon of butter to the oil.
Carefully place the sliced onions onto the griddle. Spread them out evenly to ensure they cook uniformly.
Sprinkle ½ teaspoon of garlic salt and ½ teaspoon of freshly ground pepper over the onions. Stir gently with your spatula to coat the onions evenly with the seasonings.
Allow the onions to cook for about 5-7 minutes without stirring. After that, stir occasionally, scraping the bottom of the griddle. Continue cooking for an additional 10-15 minutes, or until the onions are caramelized and tender.
Once the onions are cooked to your liking, taste them and adjust the seasoning if needed.
Remove the onions from the griddle and serve them immediately or let them cool before storing in an airtight container.