Wash the flowers under cold water. Pat dry and remove the pistils and stems. Cut into strips.
In a large skillet over medium heat, sauté the garlic in olive oil until golden. Add the anchovies and allow them dissolve.
Add the flowers, and after a few minutes, add the white wine. When the wine has mostly evaporated, mix in the mascarpone, and salt and pepper. Remove from heat.
Bring a large pot of salted water to a boil. Cook the pasta until al dente, retaining some of the cooking water. Add the pasta to the skillet with zucchini flowers. Mix in some retained cooking water until creamy. Serve immediately with a generous sprinkle of Parmigiano.