Preheat the griddle to low heat. Add olive oil to the warm griddle, then add the sliced onions. Toss to coat evenly in the oil.
Cover the onions with a dome to allow them to steam. Remove the dome and stir every 3–5 minutes to prevent burning. Continue cooking until the onions are soft and lightly golden.
Season the onions with Essential Blend seasoning, then add the white wine. Toss and cook until the wine has completely reduced and cooked off.
Add 2 tablespoons of butter to the onions and toss until fully melted and evenly incorporated. Remove from heat.
In a bowl, combine the caramelized onions with the shredded Gruyère cheese and mix well.
Spoon the onion and cheese mixture evenly onto slices of sourdough bread to assemble the sandwiches.
Melt additional butter on the griddle over medium heat. Place the sandwiches on the griddle and cook on both sides until the bread is golden and toasted and the cheese is melted.