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1
Fill a large pot with lightly salted water and bring to a rolling boil. Stir in the fettuccine, bring back to a boil, and cook pasta over medium heat until cooked through but still firm to the bite, about 8 minutes. Reserve about 1/2 cup cooking water and drain pasta.
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2
Heat 1 tablespoon olive oil in a skillet over medium heat; cook and stir 1 clove garlic in hot oil until fragrant, about 30 seconds. Add zucchini and red pepper flakes. Continue to cook and stir until zucchini are tender, about 5 minutes. Transfer vegetables to a large bowl and cover with aluminum foil.
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3
Season chicken breast halves with kosher salt and black pepper.
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4
Heat 1 tablespoon olive oil over medium-high heat in the same skillet used to cook zucchini. Pan-fry chicken in hot oil until juices run clear and center is no longer pink, about 5 minutes per side. Transfer chicken to a plate and cut into strips. Cover with aluminum foil.
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5
Whisk milk and flour together in a bowl.
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6
Heat remaining 1 tablespoon olive oil in a large saucepan; cook and stir remaining 1 clove garlic in hot oil until fragrant, about 30 seconds. Stir in flour mixture and bring to a boil while stirring constantly. Reduce heat to low and continue cooking and stirring for 2 minutes. Stir Parmesan cheese, evaporated milk, and 1/2 teaspoon salt into the flour mixture, stirring until cheese is melted and sauce is heated through, about 5 minutes. Season with salt and black pepper.
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7
Toss pasta, chicken strips, zucchini, and parsley into sauce, adding reserved cooking water as needed if sauce is too thick.
