Place a large pot of salted water on high heat and bring to a boil. Once it's at a boil, drop the pasta in and stir well. Cook for about 9-10 minutes, until al dente. Drain in a colander, but reserve a cup or so of the cooking liquid for later.
Return the pot to the stove and reduce the heat to medium. Add the olive oil, and when it starts to shimmer, add the onions. Cook, stirring occasionally, for about 5-6 minutes, until they are transluscent and start to pick up some colour on the edges.
Add the garlic and stir well for about a minute, until fragrant.
Deglaze with the white wine.
Add the cherry tomatoes, salt and tomato paste and stir well. Allow to cook down, stirring occasionally, for about 10 minutes, until the tomatoes burst and start to break down, then come together and get saucy.
Add the pasta back into the pot with a few splashes of pasta cooking water and mix mix mix everything well together until the pasta is nicely coated with the sauce. Add the basil, reserving a little for garnish, and mix again.
Portion the pasta out into plates and garnish with additional basil and gratings of cheese.