Preheat the oven to 350 degrees F.
Heat a skillet over medium-low heat and add the butter. Add the onions and garlic with a pinch of salt and stir. Cook, stirring often, for 20 to 30 minutes, until the onions start to caramelize. Once they become golden brown, remove them from the heat.
To make the brussels, heat a skillet over medium-high heat and add the olive oil. (You can do this in a separate skillet while the onions are caramelizing, or do it after in the same skillet!) Add the brussels with pinch of salt and pepper. Cook, stirring occasionally, until the brussels start to crisp up.
Place the toast slices on the baking sheet. Bake them for 10 minutes, then flip and bake for 10 minutes more. Add the grated Havarti cheese on top and return them to the oven just until the cheese is melty.
Remove the toasts and top with the caramelized onions. Top with the brussels sprouts. Spritz with a wedge of lemon, sprinkle with parmesan cheese and serve immediately.