Back at LudoBites 4.0, I fell in love with the idea of gently-cooking squid and using it instead of the pasta in carbonara, in part to delight in people's initial confusion ("Wait, where's the squid?") and in part to witness their conversion to excitement ("Wait, this is squid!").
In 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.
Prepare the circulator for 150 degrees F. Place the egg in the preheated circulator for 45 minutes. Remove the egg from the circulator and place it into an ice bath to cool off – this helps set the white part of the egg without it being watery when served. Place the chicken and the egg in the circulator for 15 minutes to rewarm them before serving.
Bring 6 to 8 quarts of lightly salted water to a rolling boil in a deep pot. Crack 1 egg into a ramekin or small bowl. Remove the pot from heat, then, using a wire whisk, stir the water briskly to create a vortex. Quickly, while the vortex remains, gently pour the egg into the center of the vortex. Allow the egg to twirl in the water until it is firm enough to remove, about 2 minutes. As the egg cooks, skim away the foam and loose pieces of egg white that float to the top. Using a slotted spoon, remove the egg from the water and set it on paper towels to remove any excess water. Repeat with the remaining eggs. Reserve the water to rewarm the eggs again just before serving them, if necessary.
Peel 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.”
Heat the lard in a sauté 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.
Heat the oil in a small sauté pan over medium-low, 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.
Place 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.