Preheat the oven to 375 degrees Fahrenheit. Line a baking sheet with parchment paper.

Slice the onion fairly thinly (but not paper-thin).

Melt 1 tablespoon of butter in 1 tablespoon of extra virgin olive oil in a large pan over medium heat. Add the sliced onions and immediately reduce the heat to low.

Cook the onions, stirring frequently, until caramelized, richly golden, and sweet. This will take 30 to 45 minutes; don’t try to rush it!

Slice the eggplant into approximately 1/2-inch rounds. Brush each one with garlic-infused olive oil on both sides, place on the prepared baking sheet, and sprinkle with salt.

Roast the eggplant until it’s tender and beginning to brown in places, approximately 30 minutes, flipping once halfway through.

Thinly slice 3 large garlic cloves. Sauté the slices very briefly in 2 tablespoons extra virgin olive oil over medium heat, just until fragrant (about 30 seconds).

Add the 8 ounces of sliced mushrooms and continue to cook over medium heat, stirring regularly, until the mushrooms give up their juices and the resulting juice just begins to dry off. This should take about 10 minutes.

Reduce the heat to low, then add the 4 ounces of goat cheese. Stir until it’s mostly melted, then turn off the heat and continue stirring until it melts completely and coats the mushrooms in a rich, thick sauce.

Spoon 1/4 cup of the San Marzano sauce onto a plate. Place an eggplant slice on top. Add a layer of goat cheese mushrooms. Top with another eggplant slice, then a layer of caramelized onions, then another eggplant slice. Spread 1/8 cup of San Marzano sauce on top of that, put another eggplant slice on top, and then top with some caramelized onions, and a bit of basil.