Heat the olive oil over medium heat in your largest skillet. Add garlic and sauté for about 20 seconds. Add broccoli, portobellos and 1/4 teaspoon salt and reduce heat to medium low. Cook, turning occasionally, until the broccoli is completely tender and melting, up to 45 minutes. Add a little more olive oil during the process if it seems advisable.
Bring a large pot of well-salted water to a rolling boil. Cook the pasta until al dente. Drain and transfer to the skillet with the broccoli, reserving a cup of the pasta water. Raise the heat to medium-high. Toss the pasta with the broccoli and mushrooms. If it seems a little dry, drizzle in some of the pasta water to develop a bit of moistness and shine. Adjust seasoning to taste.
Divide the pasta among two bowls. Sprinkle with flaky salt, freshly ground black pepper, chili flakes and grated cheese, if desired.