Prepare ingredients
Bring a medium pot of water to a boil over high heat. Rinse all produce. Roughly chop or tear basil leaves, discarding stems. Peel onion, halve, and thinly slice. Mince garlic.
Cook chicken
Heat 1 tablespoon olive oil in a large high-sided pan over medium-high heat. When oil is shimmering, add chicken and season with ¾ teaspoon salt and pepper as desired. Cook, breaking up, until browned, about 5 minutes. Add white wine and cook, scraping up brown bits from bottom of pan, until mostly reduced, 1-2 minutes more. Transfer chicken to a bowl, reserving pan drippings in pan, off heat, for Step 4.
Cook rigatoni and tomatoes
While chicken cooks, season boiling water generously with salt. Stir in rigatoni and cook for 8 minutes. Then, add whole grape tomatoes and continue cooking until rigatoni is al dente and tomatoes soften and begin to burst. Drain rigatoni and tomatoes and return to pot, off heat.
Make sauce
While rigatoni cooks, heat 1 tablespoon olive oil in pan from chicken over medium heat. When oil is shimmering, add onion and garlic and sauté, stirring, until onion is softened, and garlic is fragrant. Increase heat to medium high. Stir in tomato puree and browned chicken and simmer until flavors have melded, 3-5 minutes more. Remove pan from heat.
Finish rigatoni
Stir ¼ cup heavy cream into pan with sauce, still off heat. Season sauce with ¼ teaspoon salt and pepper as desired. Add rigatoni and tomatoes and toss to coat. Stir in baby kale to combine.
Plate chicken rigatoni
Divide creamy chicken rigatoni among serving bowls. Garnish with parmesan and basil!