Preheat your oven to 425°F (220°C). Line a sheet pan with parchment paper for easy cleanup.
Arrange the sliced cauliflower and onion on the prepared sheet pan. Drizzle with olive oil and sprinkle with salt and pepper. Toss to coat evenly. Roast in the preheated oven for about 20-25 minutes, or until the cauliflower is golden brown and tender, flipping halfway through.
While the vegetables are roasting, prepare your spread. In a small bowl, combine the light mayonnaise, minced garlic, whole grain mustard, lemon juice, and a pinch of salt and pepper. Mix until smooth and set aside.
Spread softened butter on one side of each slice of whole-grain bread. On the unbuttered side of two slices, layer the roasted cauliflower and onion, followed by the Gouda and Havarti cheese. Top with baby arugula and a generous spread of the mayonnaise mixture. Place the remaining slices of bread on top, buttered side up.
Heat a skillet over medium heat. Once hot, add the assembled sandwiches. Grill for about 4-5 minutes on each side, or until the bread is golden brown and the cheese has melted.
Once grilled to perfection, remove the sandwiches from the skillet. Allow them to cool for a minute, then slice in half and serve warm.