Cut eggplant in half and place face down on baking sheet.
Broil for 20 minutes until charred. Allow to cool slightly and scoop out the flesh. Set aside.
Bring a large pot of salted water to a boil.
Add pasta and cook for 2 to 3 minutes less than the box instructs.
Sauce
Heat the olive oil in a large saute pan with high sides.
Add the garlic and cook until fragrant, 1 to 2 minutes.
Stir in tomato paste and cook an additional minute.
Using a ladle, add about 1 1/2 cups of pasta water to the pan, stir and bring to a simmer. Allow mixture to simmer for a few minutes while the pasta finishes cooking.
Stir the eggplant into tomato paste mixture, add more pasta water if needed and stir until well combined.
Simmer for 3 to 4 minutes.
Add pasta directly from the pot and coat with sauce. Add the cheese and fold in the basil.
