Pour the tomatoes and their juice into the insert set in a 5-, 6-, or 8-quart Instant Pot. Use your clean hands to crush the tomatoes into smaller bits. Get in there! You know you want to!
Press Sauté and set it for Medium/Normal or Custom 300°F and set the time for 10 minutes.
As the pot heats, stir in the broth, garlic, salt, and nutmeg. Add the butter. Cook, stirring occasionally, until the butter melts and the entire mixture gets steamy, on the edge of simmering, about 5 minutes.
Turn off the heat and lay the broken spaghetti in a crosshatch pattern on the top of the sauce. Press down gently so some of the pasta is in the sauce but none of it touches the insert’s bottom. Lock the lid on the pot.
MAX model: Set the pot for Pressure Cook on MAX pressure for 4 minutes.
Other Instant Pot models: Set the pot for Pressure Cook/Manual on High pressure for 6 minutes.
When the pot has finished cooking, use the quick-release method to bring the pressure back to normal. Unlatch the lid and open the cooker. Stir well, then set the lid askew over the pot and set aside for 2 to 3 minutes so the pasta continues to absorb some of the excess sauce. Serve warm, garnished with finely grated Parmigiano-Reggiano.