Bring a large pot of water to a boil. Add a generous pinch of salt and add the orzo. Cook until just shy of al dente, about 7 minutes. Scoop out ¼ cup of the pasta water and set it aside. Drain the pasta and set aside. Note: If you’re worried about the orzo sticking, you can cook the pasta in one pot and begin the sauce in a second pot.
Wipe out the pot and return it to the stovetop.
Make the sauce:
Turn the heat on the pot to medium and add the mushrooms. Cook for 5–7 minutes until they begin to release their liquid. Add the extra virgin olive oil and the red onion. Cook, turning often, until the mushrooms deepen in color and the onion softens, about 7–9 minutes.
Add the garlic, a pinch of sugar, and a pinch of crushed red pepper to the pot. Cook for 1 minute until fragrant.
Pour in the crushed tomatoes and balsamic vinegar and bring to a boil. Reduce heat to medium-low and simmer the sauce rapidly for 10–15 minutes. If the sauce begins to stick or evaporates too quickly, add a splash of water and reduce the heat to low. Taste and add salt, pepper, sugar, or crushed red pepper to taste.
Finish the sauce:
Add the chopped spinach to the pot and cook for 2–3 minutes. Add the orzo and toss to coat. Cook for 1–2 minutes until the orzo is well coated, adding a splash of pasta cooking water as needed. Taste and season. Turn off the heat.
To serve:
Divide the orzo between shallow bowls and drizzle with smoked olive oil. Enjoy!