Step 1:
Cut 2 pounds boneless beef chuck into 4 pieces.
Heat 1 tablespoon of the olive oil in a large heavy-bottomed pot over medium-high heat until shimmering.
Add the chuck and sear until golden-brown all over, 8 to 10 minutes total.
Transfer to a plate.
Step 2:
Reduce the heat to medium.
Add 1 tablespoon of the olive oil and 1 pound uncooked sweet or hot Italian sausage links to the pot.
Sear until golden-brown all over, about 5 minutes total.
Transfer to the plate with the chuck.
Step 3:
Remove the pot from heat and let cool slightly, about 2 minutes.
Meanwhile, finely chop 5 garlic cloves (about 2 tablespoons) and pick the leaves from 3 to 4 large fresh basil sprigs until you get 1/4 packed cup.
Step 4:
Return the pot to medium heat, add the remaining 2 tablespoons olive oil, and heat until shimmering.
Add the garlic and cook, stirring frequently, until light golden-brown, about 1 minute.
Step 5:
Add 3 tablespoons tomato paste and continue to cook, stirring frequently, until the tomato paste has darkened in color, about 1 minute.
Step 6:
Pour 2 (28-ounce) cans whole peeled tomatoes and their juices.
Fill half of one of the empty tomato cans with water and pour the water into the pot.
Using a wooden spoon or potato masher, break up the tomatoes into small bits.
Add the basil leaves and season with 1 1/2 teaspoons kosher salt, 1 teaspoon granulated sugar, and 1/4 teaspoon black pepper.
Step 7:
Increase heat to medium-high and bring the sauce to a rapid simmer.
Return the chuck, sausages, and any accumulated juices to the pot.
Reduce the heat to low and partially cover the pot.
Gently simmer, stirring occasionally, until the chuck is falling apart, 3 1/2 to 4 hours.
Step 8:
Transfer the chuck and sausages to a clean cutting board or plate.
Shred the chuck with two forks into bite-sized pieces and cut the sausages into thick slices on a slight diagonal; return both to the sauce. (Alternatively, leave the meat whole and transfer to a platter, and use the sauce to sauce the pasta, serving the meat on the side for individuals to add to their plate and shred or cut as they want.)
Step 9:
Taste and season the sauce with more kosher salt and black pepper as needed.
If the sauce tastes too tangy or acidic, add more granulated sugar 1/2 teaspoon at a time.
Serve the sauce over cooked spaghetti.
