Bring a large pot of salted water to a boil.
When the water’s boiling, add the pasta and cook according to package directions.
Reserve 1 cup of pasta water and then drain.
Meanwhile, in a large skillet, heat the olive oil over medium-high.
Add the tomatoes, season with salt; cook, shaking occasionally, until charred and wrinkly; 4 to 6 minutes.
Transfer to a large bowl to cool.
In a liquid measuring cup, stir together the tahini and grated Parmesan cheese; season with salt and pepper; mixture will be thick.
When the pasta is drained, add ½ cup pasta water to the dressing and stir until smooth.
Add the pasta to the bowl with the tomatoes; stir in enough dressing to coat; save remainder for a later step in this recipe.
Let cool for 15 minutes or up to 3 hours at room temperature.
When ready to serve, stir the remainder of the dressing into the pasta.
Stir in the water which was reserved from the pasta water or use tap or bottle water, as needed, until the pasta is glossy and creamy.
Stir in the mint, scallions, sesame seeds and chopped Parmesan cheese, reserving a little for garnish if desired.
Season to taste with salt, pepper and a drizzle of olive oil.
