Bring a large pot of well salted water to boiling.
In a large skillet warm 2 tablespoons of oil over high heat. Add half the zucchini, season with salt, and cook, without moving it, until dark golden, about 2 to 3 minutes. Transfer the zucchini to a paper towel lined plate. Add another 2 tablespoons of oil to the skillet and repeat with the remaining zucchini. Add 2 Tablespoons of water to the pan and remove from heat.
Cook the pasta according to the package instructions until 2 minutes shy of al dente; drain.
In the same skillet, melt 3 tablespoons of butter over medium heat. Add the garlic and cook 2 to 3 minutes. Toss in the penne and zucchini, and cook until the pasta is al dente, about 2 or 3minutes, adding more water if the sauce is dry. Toss in 1/4 cup of the parmesan and the remaining tablespoon of butter, add the mint and season to taste with salt and pepper.
Divide the pasta among four bowls and finish each with a drizzle of oil and a it of cheese.