Heat grill to 350°F or stove top grill pan over medium high heat. Place sausages on the grill, cover and cook, turning occasionally until they are cooked through, 8 to 10 minutes. If using a grill pan cook 4-5 minutes per side, or until cooked through. Set aside and keep warm.
Bring a large pot of heavily salted water to a boil. Cook pasta for 11 minutes. Reserve 1 cup of pasta water, set aside and start the sauce.
Heat the oil over medium high heat in a skillet and sauté the onion for for 5 minutes. Add the garlic, kosher salt and red pepper flakes. Stir and cook another 2 minutes.
Add tomato paste and stir, scraping up browned bits. Cook this for 5 more minutes. Deglaze the pan with the vodka, stirring constantly and then add the heavy cream. Stir until smooth and creamy. The sauce with be a bright orange. Season to taste.
Drain pasta, but do not rinse it. Put it back into the large pot with the reserved cup of pasta water and pour vodka sauce on top. Stir to coat and simmer for a few minutes, or until sauce thickens and is shiny and emulsified.
Serve immediately with grilled sausages, basil leaves to garnish, lemon slices and top with freshly grated parmesan cheese.