In the pot you'll cook and serve from, whisk the gochugaru, gochujang, garlic, soy sauce, and kimchi brine into a rough paste at the bottom.
Arrange the Spam, sausage, tofu, onion, and chopped kimchi around the pot in sections rather than stirring them together — this is the traditional presentation and it also makes portioning easier once everyone's eating from the same pot.
Pour the stock in gently around the edges, trying not to disturb the arrangement too much.
Bring to a boil over medium-high heat, then lower to a steady simmer for 8 to 10 minutes, until the kimchi has softened and the broth has taken on color from the gochugaru and gochujang.
Taste the broth and adjust — saltiness varies a lot depending on your kimchi and stock, so add a little more gochujang or soy sauce rather than trusting the measurements exactly.
Nestle the instant noodle block into the broth and simmer 3 to 4 minutes, just until the noodles loosen and turn tender. Don't walk away here — instant noodles overcook fast and turn mushy within another minute or two.
Lay the cheese slice over the top in the last 30 seconds if using, letting the residual heat melt it into the broth.
Scatter the scallion over the top and serve straight from the pot, ideally still at a gentle simmer, with rice on the side.