Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally until cooked through but firm to the bite, about 12 minutes. Drain spaghetti and transfer to a serving bowl.
Heat Italian dressing in a large skillet over medium-low heat; cook and stir broccoli, cauliflower, and carrot in the dressing until slightly tender, about 5 minutes. Add mushrooms and parsley to vegetable mixture; cook and stir until tender, about 5 minutes more.
Mix milk and mayonnaise together in a microwave-safe bowl; heat in microwave until warmed, 30 seconds to 1 minute. Stir milk mixture into vegetable mixture; cook until heated through, 1 to 2 minutes.
Spoon vegetable mixture over spaghetti and top with Parmesan cheese and almonds.