Heat the olive oil in a large pot over high heat until shimmering.
Add the diced onion and red pepper and cook 3–5 minutes, stirring occasionally, until the onion is translucent; push the vegetables to the sides of the pot.
Add the ground beef to the center of the pot and sear about 1 minute per side, then break it up with a wooden spoon and cook until mostly browned with a little pink remaining.
Stir in the minced garlic, tomato paste, taco seasoning, and beef bouillon powder; season with salt and pepper (about 1/4 tsp salt and 3/4 tsp pepper if using the suggested amounts). Cook until beef is fully browned and fragrant.
Pour in the canned tomatoes, enchilada sauce, and chicken broth and bring the mixture to a full boil.
Break the spaghetti in half and submerge the pieces in the boiling liquid. Reduce heat slightly so it continues to boil gently, and cook 10–12 minutes, stirring often and scraping the bottom to prevent sticking.
About 8–10 minutes into cooking, lower the heat to medium if the liquid is evaporating too quickly; add a splash of extra broth if the sauce becomes too thick before the pasta is tender.
When the spaghetti is al dente, remove the pot from heat. Toss the pasta with tongs for about a minute so the sauce thickens and the pasta finishes cooking.
Allow the mixture to cool slightly, then add the shredded Cheddar 1/4 cup at a time, tossing until fully melted and evenly incorporated.
Serve immediately.