Heat a heavy-bottomed saucepan over medium heat. Add in Onions and 1 tbsp Olive oil. Cook for 1 minute until heated through, then turn the heat down to low and add in 1/4 cup water, remaining Olive Oil, and salt. Cook, stirring occasionally, for 1 hour.
The Onions will go from White to translucent, and finally will begin to turn golden brown. If the Onions are looking dry, add 1-2 additional tbsp of water, as necessary. Once Onions have reached a nice medium golden brown color, remove from heat and allow to cool slightly. They can be stored for up to 1 week in the fridge.
Prepare the Grilled Cheese
Heat a skillet over medium heat. Spread Mayonnaise over both slices of bread, then spread Mustard Sauce over the opposite side of one of the slices.
Place both slices, Mayonnaise side down, onto skillet. Dollop the Mustard on a slice of bread with Caramelized Onions and sprinkle on a few leaves of fresh Thyme. Carefully place grated Gruyere over the other slice. Cook for 2-3 minutes, until Cheese is melted completely. Press Sandwich together and serve with sliced Tomatoes and Shredded Cabbage.