Toasting gives dishes a nutty undertone.
In a medium saucepan, bring the stock to a boil, then reduce heat to low and keep warm.
In a large, deep skillet, heat the oil, two turns of the pan, over medium-high. Add the butter and let it melt into the oil. Add the pasta; cook, stirring often, until golden and fragrant, 2 to 4 minutes [1, above]. Add the onion and garlic and cook, stirring often, until softened a bit, 2 to 3 minutes. Season the pasta with salt and the crushed red pepper and add the bay leaf. Add the vodka and cook, stirring constantly, until fully absorbed, about 1 minute. Add 1 1/2 to 2 cups stock (a few ladlefuls), the cherry tomatoes [2, above] and half the passata; stir until the liquid is greatly reduced but not dry, 5 to 6 minutes. Add the remaining stock [3, above], the remaining passata and the basil.
Cook, stirring often, until the sauce is reduced and the pasta is al dente, adding water by the quarter cupful if the sauce reduces before the pasta is cooked, about 10 minutes more. Stir in about 1 cup cheese. Serve the pasta in shallow bowls, passing more cheese at the table.