Preheat the oven to 400°F.
On a large baking sheet, gently toss the cauliflower slices and onion rounds with the olive oil. Arrange them in a single layer and season with salt and freshly ground black pepper to taste.
Roast in the preheated oven for 20 minutes, or until the cauliflower is golden brown and tender. Remove from the oven and set the roasted cauliflower and onions aside to cool to room temperature (or at least a few minutes so they are not piping hot).
While the vegetables cool, make the aioli: in a small bowl combine the light mayonnaise, minced garlic clove, whole grain mustard, and fresh lemon juice. Stir until smooth and season with salt and freshly ground black pepper to taste.
Spread the softened butter on the outside (one side) of each slice of whole-grain bread. On the opposite, unbuttered side of each slice spread an even layer of the aioli.
Assemble two sandwiches: place one bread slice aioli-side up and layer in this order — Arla Dofino® Gouda (use the 2 slices or 2 ounces grated as listed), roasted cauliflower pieces, roasted onion rounds, Arla Dofino® Creamy Havarti (use the 2 slices or 2 ounces grated), and finish with the baby arugula. Top with the remaining bread slice, buttered side out.
Heat a large skillet or griddle over medium heat. When hot, place the assembled sandwiches in the skillet, buttered side down.
Cook the sandwiches for 4–6 minutes on the first side, until the bread is golden brown and the cheese begins to melt. Gently press with a spatula as needed for even contact.
Carefully flip each sandwich and cook for an additional 3–4 minutes, until the second side is golden brown and the cheese is fully melted.
Remove sandwiches from the skillet, cut in half, and serve immediately.