In a wide skillet, add the butter and olive oil and heat over medium heat until the butter begins to melt. Add all the onions along with a generous pinch of kosher salt. Cook for 3 to 4 minutes over medium heat until the onions begin to soften. Then turn down the heat to medium low.
Cook the onions over medium low heat until they are very tender and a deep brown colour. Keep an eye on the onions, stirring regularly, to ensure they caramelize evenly and do not stick to the pan. Add a bit more olive oil if the onions begin to stick. The onions will take about 45 minutes.
When the onions are fully caramelized, add the balsamic vinegar, salt, and pepper. Cook for another couple of minutes until the vinegar has reduced.
Place a non-stick skillet over medium heat. Lightly spread butter on both sides of the bread slices. Arrange the bread slices in the skillet. Cook until the bread is well toasted and golden brown and then flip over. Transfer the toasted bread to a rack and set aside until ready to assemble.
Turn the broiler on high. Arrange the toasted bread on a baking sheet. Top with a pile of the caramelized onions. Combine the grated Gruyère and Parmesan cheeses. Cover each toast with a mound of shredded cheese. Broil the toasts for 4 to 6 minutes until the cheese is melted and begins to brown. If desired, garnish with chopped fresh parsley and enjoy!