Heat butter and 1 Tbsp. of the olive oil in a large skillet over medium heat. Once hot, add two cloves of the minced garlic, and cook 1 minute, until aromatic. Stir in breadcrumbs and 3 Tbsp. of the Parmesan cheese; cook until golden and toasted, stirring occasionally, about 4 to 5 minutes. Transfer breadcrumbs to a bowl and return pan to medium heat.
Add remaining 1 Tbsp. oil to pan. Once hot, add pancetta, and cook 3 to 5 minutes, until crispy. (While pancetta cooks, this is a good time to bring a large pot of salted water to a boil.) Add shallots, remaining 2 garlic cloves, chili flakes, salt, and pepper to pan with pancetta; cook 2 to 3 more minutes, until shallots soften. Stir in kale; cook 1 to 2 minutes, until leaves start to soften.
Add San Marzano tomatoes and white beans to pan; stir to combine. Cover, and gently simmer over medium-low heat. At this point, your pasta water should be boiling. Add the spaghetti and cook until al dente. Prior to draining, reserve 1 cup of pasta cooking water, and drain remaining. Return spaghetti to pot, and carefully pour skillet of pomodoro sauce over spaghetti. Gradually stream in reserved pasta cooking water, tossing constantly, until sauce begins clinging to noodles. Sprinkle in remaining 3 Tbsp. parmesan cheese. Adjust seasonings as needed.
Arrange a serving of pasta on a plate, and garnish with fresh basil and a spoonful of garlicky breadcrumbs.