To make the pomodoro sauce, in a large, deep sauté pan or a large saucepan over medium heat, combine the tomatoes and juices, butter, onion, garlic, Parmesan rind and 2 tsp. salt. Bring to a simmer and cook, uncovered, stirring occasionally and crushing the tomatoes as they cook down, until the tomatoes are mostly crushed and the sauce is reduced slightly, 1 to 1 1/2 hours. Remove the pan from the heat and discard the onion and Parmesan rind.
Let the sauce cool slightly, then transfer to a blender and blend until smooth, about 1 minute. The sauce can be made up to 4 days in advance; let cool completely, then cover and refrigerate until ready to use.
Return the sauce to the pan and season to taste with salt and pepper. Set the pan over low heat to keep warm.
To make the pesto, in a food processor, combine the Parmesan and pine nuts and process until ground. Add the basil and pulse until finely chopped. With the processor running, pour in 3/4 cup (6 fl. oz./180 ml) of the olive oil and process until blended, then stir in the remaining 1/4 cup (2 fl. oz./60 ml) oil. The pesto will be slightly loose and oily. Season to taste with salt and pepper. The pesto can be made up to 4 days in advance; cover and refrigerate until ready to use. Bring to room temperature before serving.
Meanwhile, bring a large pot of heavily salted water to a boil over high heat. Add the pasta and cook according to the package instructions until al dente. Using a spider or a fine-mesh strainer, transfer the pasta directly from the cooking water to the pan with the pomodoro sauce, sprinkle with the Parmesan and toss to coat. For a thinner sauce, add 1/4 to 1/2 cup (2 to 4 fl. oz./60 to 125 ml) of the pasta cooking water and cook until silky and emulsified.
Transfer the pasta and sauce to a serving platter or plate and drizzle with the pesto. Sprinkle with pecorino sardo, garnish with basil leaves and serve immediately.