Preheat the oven to 400˚F.
Spread the tomatoes out on a baking sheet, and toss lightly with olive oil. Season generously with salt and pepper. If the tomatoes aren’t very sweet, sprinkle them with a pinch of sugar. If you have any sprigs of thyme hiding in the vegetable drawer, throw them on. Bake until the tomatoes start to shrivel and collapse, giving the pan a shake once or twice while cooking, about 18-20 minutes. Do Ahead: The tomatoes can be made up to 4 hours in advance. Store at room temperature.
In the meantime, bring a large pot of salted water to a boil. Once the tomatoes are done, cook the pasta to “al dente” according to package directions. Reserve 1 cup of the pasta water, then drain the pasta. Put the noodles back into the pot over medium-low heat. Add the butter and the kale pesto. Toss to coat. Add ¼-1/2 cup of the cooking liquid to create a smooth sauce. Fold in the tomatoes. Remove the pot from the heat and add a handful of freshly grated Parmesan cheese along with salt and pepper to taste. If the pasta looks dry, add a bit more of the cooking water. Divide the pasta into bowls and garnish with more Parmesan. Serve!