Step 1
Warm ¼ cup vegetable oil and 4 garlic cloves, thinly sliced, in a medium pot over medium heat. Cook, stirring often, until garlic is beginning to turn golden, about 3 minutes. Stir in 1 Tbsp. black or white sesame seeds and cook, stirring occasionally, until garlic is golden brown and crisp, about 1 minute. (Don’t walk away; this happens fast, and the garlic can go from perfect to burned in seconds.) Transfer mixture to a small bowl and stir in 1 Tbsp. gochugaru or 1½ tsp. crushed red pepper flakes; season with kosher salt. Set garlic oil aside for serving. Wipe out pot and reserve.
Step 2
Trim dark green parts from 4 scallions and thinly slice; set aside for serving. Coarsely chop white and pale green parts. Heat remaining 2 Tbsp. vegetable oil in reserved pot over medium-high. Cook chopped scallions and one 2″ piece ginger, peeled, thinly sliced, stirring often, until scallions are charred in spots, about 4 minutes. Add 2 Tbsp. tomato paste and cook, stirring occasionally, until it begins to stick to the bottom of pot and darkens slightly, about 2 minutes. Add 8 dried shiitake mushrooms and one 4×3″ piece dried kombu, then stir in 5 cups cold water. Bring to a boil, then remove from heat and let sit until mushrooms soften, about 10 minutes. Remove and discard kombu.
Step 3
Using a slotted spoon, transfer solids to a blender. Add 1 or 2 ladlefuls of broth to blender and purée until smooth. Stir purée back into broth in pot and bring to a simmer over medium heat. Add 3 Tbsp. unsalted butter, one tablespoon at a time, whisking to combine after each addition before adding more. Stir in 1 Tbsp. low-sodium soy sauce, taste, and season with kosher salt if desired. Reduce heat to low and keep warm until ready to serve.
Do ahead: Ramen broth can be made can be made 5 days ahead. Let cool; transfer to an airtight container and chill (or freeze for up to 3 months). Reheat over medium until warmed through; whisking to re-emulsify.
Step 4
Meanwhile, bring a large pot of water to a boil. Add 4 baby bok choy (about 12 oz. total), quartered lengthwise, and cook until bright green and tender, about 2 minutes. Using a slotted spoon, transfer bok choy to a plate. Return water to a boil and cook four 5-oz. packages fresh ramen noodles according to package instructions. Drain and divide among bowls.
Step 5
To serve, ladle broth over noodles, then top with bok choy and reserved garlic oil. Top with jammy eggs, toasted nori sheets, and/or cilantro (if using).