Cook the ground chicken in a large saucepan with 2 teaspoons olive oil and Italian seasoning and red pepper flakes until crumbly and fully cooked. Season with salt and pepper. Remove and set aside.
Heat the oil and butter in the same saucepan over medium-high heat. Once the butter has melted, add the onions and cook, stirring frequently, until softened but not browned, about 3 minutes. Add the garlic, oregano and crushed red pepper flakes; cook, stirring, until fragrant, about 1 minute. Add the crushed tomatoes, with their juices. Bring to a boil over high heat, then reduce the heat to medium-low so the mixture is barely bubbling; cook for 20 to 30 minutes, stirring occasionally, until the sauce has thickened and reduced to 4 cups. Season with salt and pepper.
Working in batches as needed, transfer the sauce to a blender. Add the cream and vodka. Remove the center knob on the lid (to allow steam to escape); place a towel over the lid to prevent spilling. Starting on the lowest speed and gradually increasing to high, blend until completely smooth, about 30 seconds. Return to the saucepan and bring just to a boil over high heat, then reduce to medium-low and cook, allowing the sauce to reduce and the vodka to cook off.
Cook the pasta until al dente. Drain the pasta, reserving 1 1/2 cups of the cooking water, then return the pasta to the pot with the sauce and add the chicken. Stir to combine, and cook over medium heat, stirring frequently, adding some of the reserved pasta cooking water as needed to thin it out.
Serve right away, topped with basil and grated cheese (to taste). Season with salt and pepper to taste