In a saucepan, toss the mussels with oil, chili pepper, pepper, and lemon juice. Strain the mussel water and set aside.
Meanwhile, cook the pasta in plenty of salted water until al dente, remembering to set aside a little for the final topping.
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In a nonstick saucepan, bring the milk to a boil and pour in the mozzarella, previously diced. Add the cornstarch and stir until the fondue is the desired consistency.
Drain the pasta and add it to the mussel sauce. Finally, add the fondue, a drizzle of oil, and pepper, and serve. Finally, a generous grating of lemon zest and you're done.