Make the chorizo breadcrumbs. Chop the chorizo into small chunks. Heat 1 tablespoon of oil in a saute pan over medium heat. Add the chorizo and saute until browned, about 3-4 minutes. Add the breadcrumbs and stir to combine. Continue to cook until the breadcrumbs become golden brown. Remove from heat and drain the chorizo breadcrumbs on paper towels.
Melt 1 tablespoon of butter in a large saute pan over medium heat. Add 2 cups chopped kimchi with its juices in the pan and saute until caramelized, about 5 minutes. Add gochujang, stirring to combine. Add coconut milk and simmer for 5 minutes.
Cook spaghetti according to directions on package. Drain the pasta, reserving 1 cup pasta water.
Add the pasta to the kimchi sauce along with ½ cup pasta water, ½ cup grated parmesan, and butter. Stir to combine and season with salt and pepper. If the pasta sauce is too thick, add additional water.
Portion the pasta into bowls and top with a poached egg and chopped scallions. Top with extra parmesan if desired. Serve immediately.
Notes
You can prepare the chorizo breadcrumbs up to 3 days in advance. Store in the refrigerator until ready to use.