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Heat ¼ cup oil in a large skillet over medium-high. Cook almonds, tossing frequently, until lightly golden, 1–2 minutes. Using a slotted spoon, transfer almonds to a medium bowl, leaving that almondy-oil goodness in the skillet.
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Let almonds cool 10 minutes. Toss with parsley, lemon zest, and 2 Tbsp. Parmesan; season with salt and pepper. Set aside.
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Add remaining 2 Tbsp. olive oil to almond oil in skillet. Heat over medium-high and cook mushrooms, undisturbed, no matter how much you may wish to give them a toss, until browned on 1 side, about 2 minutes. Toss and continue to cook, undisturbed, until browned on underside, about 2 minutes. Season with salt and pepper and continue to cook, tossing occasionally, until mushrooms are tender but still retain their shape and have some bite, about 2 minutes more.
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Add leeks and garlic, season with salt and pepper, and cook until leeks are bright green and just getting tender, 4–5 minutes. Add stock and bring to a simmer.
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Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente, 8–10 minutes. Drain and transfer to skillet with mushroom mixture. Add remaining ⅓ cup Parmesan and cook, tossing, until sauce is nice and silky and creamy and lightly coats pasta, 2–3 minutes.
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Serve pasta topped with reserved almond mixture.