Bring a medium sized pot of water to a boil over medium high heat. Gently lower eggs into the boiling water, turn down the heat to simmer, and set a timer for 7 minutes. When the timer rings, remove eggs from simmering water and shock in ice bath. Peel eggs and quarter lengthwise.
Make Spicy Caesar Dressing
Place garlic, lemon juice, gochujang, apple cider vinegar, gochugaru, anchovies, and soy sauce in a blender or food processor. Pulse a few times, then blend until well combined and smooth.
With the blender running, slowly stream in the olive oil and avocado oil. Transfer the Spicy Caesar Dressing to a container. You will use only about half of it.
Assemble the Little Gem Salad
In a large bowl, drizzle the Little Gem lettuce leaves with about ½ cup of the Spicy Caesar Dressing. Toss to evenly coat. Your hands are probably the best tool here, as you can massage the dressing into the little folds in the leaves.
Transfer the Little Gem lettuce leaves to serving plate and sprinkle with the pistachios. Top with the quartered eggs. Sprinkle with shredded Parmigiano-Reggiano and chopped fresh parsley if using. Serve extra dressing alongside.