Bring a large pot of heavily salted water to a boil over medium-high heat. Meanwhile, prepare the sauce.
Halve 12 to 13 ounces beef sausage lengthwise, then cut crosswise into thin half-moons. Trim and thinly slice 1 medium green bell pepper, 1/2 medium yellow onion, and 3 garlic cloves.
Place 1 tablespoon of the unsalted butter in a small microwave-safe bowl and microwave until melted. Alternatively, melt in a small saucepan on the stovetop. Add 1/4 cup of the ketchup, 2 tablespoons oyster sauce, and 1 teaspoon hot sauce. Stir to combine.
Heat 2 tablespoons olive oil in a large skillet over medium heat until shimmering. Add the garlic and cook, stirring occasionally, until fragrant, about 30 seconds. Add the onion and beef sausage and cook until the onion is slightly translucent, 2 to 3 minutes. Add the bell pepper, season with 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper, and cook until the pepper softens, about 2 minutes.
Push the vegetables to the sides of the pan to make a well in the middle. Pour the ketchup mixture into the well and cook undisturbed until the sauce is lightly caramelized, about 30 seconds. Stir everything together and let simmer until the sauce thickens, 3 to 5 minutes. Remove the pan from the heat.
Meanwhile, add 1 pound dried spaghetti to the boiling water and cook according to package directions until 1 minute less than al dente. Reserve 1 cup of the cooking water. Drain the pasta.
Add the drained pasta and 1/2 cup of the cooking water to the sauce. Toss with tongs over medium-low heat until the sauce coats the noodles. Add the remaining 1 tablespoon unsalted butter and 1 tablespoon ketchup, adding more of the pasta water a tablespoon at a time as needed if the sauce is too thick. Serve garnished with shaved Parmesan cheese.