Mash together the softened butter, minced anchovies, minced garlic, and lemon zest until fully combined. Set aside.
Bring the broth to a simmer in a pot and stir in the soy sauce.
Bring a separate pot of water to a boil and cook the ramen noodles according to package directions. Drain and divide between two bowls.
Pat the squid rings completely dry with paper towels.
Heat the vegetable oil in a skillet over high heat until shimmering. Add the squid in a single layer and sear for 60 to 90 seconds per side, until just opaque. Remove immediately and set aside.
Whisk the anchovy butter into the simmering broth, a spoonful at a time, until fully melted and glossy.
Ladle the hot broth over the noodles in each bowl.
Top each bowl with the seared squid, a halved soft-boiled egg, sliced scallions, and torn nori.
Serve immediately while the broth is still steaming.