Step 1 Make fresh pasta dough by pulsing the flour and 4 teaspoons olive oil in a food processor. Add the egg and pulse until the dough forms a ball that rides around on the top of the blade. Remove the dough from the food processor and knead until smooth and shiny; this should take only about a minute. Wrap in plastic wrap and refrigerate at least 1 hour.
Step 2 Roll the pasta dough very thin on a pasta machine, about a 6 setting on most machines, flouring as necessary. The sheets should be at least 4 inches wide. Cut the pasta sheets into squares, dust lightly with flour and set aside until ready to use.
Step 3Cook four or five pasta sheets at a time in plenty of rapidly boiling salted water. The pasta will be done when the sheets float to the surface, 1 to 2 minutes. Remove from the boiling water and drain on a tea towel if using immediately, or transfer to a large bowl of water to store. Repeat using all of the pasta.
Step 4Heat a stove top or grill pan over medium-high heat. Trim the ends from the zucchini and slice lengthwise into strips about one-eighth-inch thick. In a large, shallow bowl, toss the zucchini with 3 tablespoons olive oil and one-fourth teaspoon salt. Place the zucchini strips on the grill and grill for about 2 minutes on each side, until the zucchini is softened and has defined grill marks. Set aside.
Step 5Heat 2 tablespoons olive oil in a medium skillet over medium-high heat. Add the onions and cook until softened, about 5 minutes. Add the white wine, garlic and thyme leaves and cook until aromatic, about 2 minutes. Add the zucchini strips and toss. Season to taste, then remove from heat and set aside.
Step 6In a small saucepan, simmer the cream over medium-low heat with thyme sprigs, lemon zest, one-half teaspoon salt and 1 tablespoon of the grated Parmigiano-Reggiano. Cook until the cream reduces slightly, about 10 minutes.
Step 7In a small bowl, beat together the ricotta, one-fourth teaspoon salt, garlic and parsley until mixed. (The dish can be prepared to this point at least 1 hour ahead of time. The zucchini and cream sauce can be held at room temperature. Cooked pasta sheets should be stored in a large bowl of water and drained and patted dry before using.)
Step 8Place the cooked pasta in a large mixing bowl and pour the cream sauce through a fine strainer over the pasta. Mix gently to lightly coat the pasta squares. Place one pasta square on an oven-proof plate and spoon about 3 tablespoons of ricotta in the center. Arrange a few strips of zucchini on top. Place another pasta square on top of that. Sprinkle with some of the remaining grated Parmigiano-Reggiano, and scatter more zucchini over the top. Repeat with three more plates.
Step 9Place the plates on a cookie sheet and place in the oven to heat through, about 10 minutes. Serve immediately.