Step 1In a medium pot over medium-high heat, reduce the chicken broth and heavy cream by three-fourths. Stir in the Parmesan cheese and whisk until incorporated. Remove from heat and set aside. This makes about 1 cup sauce, more than is needed for the recipe. Cover and refrigerate the sauce for up to 3 days.
Step 1Peel the membrane from the squid heads. Slice the head lengthwise along the tube and lay the squid flat. Slice the squid into one-fourth-inch slices to make "noodles."
Step 2Heat the lard in a saute pan over medium heat, add the lardons and cook until they are lightly crisp on all sides, about 3 to 5 minutes. Remove from heat and set aside on a paper towel.
Step 3In a small saute pan heated over medium-low heat, add the olive oil, swirling it around the base of the pan. Place the squid in the pan and cook quickly until just opaque, about 10 to 15 seconds, and remove to a paper towel.
Step 4Place half the squid in the center of each of two plates. Place 2 tablespoons Parmesan sauce over each plate of squid. Place a poached egg on top of the squid and sprinkle ground pepper over the eggs. Place half the lardons around the squid on each plate. With your hand up high, sprinkle a tablespoon of Parmesan onto each plate so it looks like snow. Sprinkle chive flowers or chives for garnish. Serve immediately.