Bring a medium (4-litre) pot of water to a boil over high heat. Add enough salt so the water is pleasantly salty, followed by the pasta, and cook according to the package instructions until al dente. Reserve 1 cup of the pasta cooking water, and drain the pasta.
Meanwhile, in a large (30cm), deep skillet or saute pan over medium heat, heat the oil and melt 1 tablespoon of the butter. Add the shallot and cook, stirring occasionally, until it starts to soften, 3 to 5 minutes.
Add the mushrooms and pepper and cook, stirring occasionally, until the mushrooms release their liquid and it evaporates and the mushrooms start to brown, 5 to 7 minutes.
Add the garlic, miso, vinegar and soy sauce and stir to combine. Add the reserved pasta cooking water, increase the heat to medium-high to bring the mixture to a boil, then reduce the heat so the sauce is gently simmering.
Add the remaining 6 tablespoons of butter, 1 piece at a time, stirring constantly until the sauce emulsifies and thickens slightly, about 3 minutes.
Add the cooked pasta and toss to combine. Stir in the spinach (in batches, if necessary) and cook, tossing or stirring gently, until wilted, 1 to 2 minutes.
Taste, and season with more salt and pepper, as desired. Serve warm, sprinkled with shichimi togarashi, and with lemon or lime wedges for squeezing over the top.
