Bring a large pot of salted water to a boil over high.

Heat a 12-inch skillet (preferably stainless steel, or one with a light colored cooking surface, so you can monitor the butter as it browns) on medium-high. When hot, drizzle with olive oil and then add the brussels sprouts and garlic. Season with salt and pepper and cook, stirring frequently, until the brussels sprouts are tender and caramelized around the edges, 6 to 7 minutes.

Scrape the brussels sprouts into a bowl, ensuring that the skillet is as clean as possible. (You may need to rinse or wipe it out, but take care, as the pan will be very hot.)

Add the pasta to the boiling water and cook according to the package instructions until al dente. Drain and reserve ½ cup of pasta cooking water.

Place the skillet back on medium-high heat. Add the butter, swirling the pan to encourage it to melt. Once it has melted, continue swirling gently, until the milk solids turn a deep golden brown and smell nutty; this should only take 4 to 6 minutes. Remove immediately from the heat and allow it to cool for 1 minute. Very carefully drizzle in the soy sauce (it may sizzle) and add the white parts of the scallions. Stir to lift any burnt bits stuck to the pan.

Add the pasta and the Brussels sprouts to the soy sauce-brown butter, along with 2 to 3 tablespoons of pasta cooking water, and place on medium heat, tossing until the strands are well coated, about 2 minutes.

To serve, place the pasta into serving bowls, and season generously with pepper. Top with grated Parmesan and the green parts of the scallions.