For the chicken bacon:
The day before you plan to serve this dish, mix the sugar, salt and allspice in a bowl. Generously season the chicken thighs on both sides with the spice mix. Lay them on a tray, wrap the tray in plastic wrap, and refrigerate it overnight. The next day, rinse the chicken in cold water.
Light the briquettes outside in a grill. Once they are hot, take the hay out of the water, wring it out, and place it on top of the charcoal. Lay the chicken, skin side down, on the grill. Cover the grill and smoke the chicken for 20 minutes. Remove it from the grill and chill it in the refrigerator.
When you are ready to assemble the dish, cut each chicken thigh in half. Lightly season it with salt and pepper. Heat the olive oil in a skillet over medium heat. Cook the chicken thighs on both sides until cooked through.
Note: Bacon lardons or grilled chicken thighs may be used in place of chicken-thigh bacon.
For the potato "risotto":
Combine the potato and cream in a wide pan and cook over medium heat, stirring constantly, until the potato achieves an al dente consistency. Finish with pecorino and season with salt, if needed.
For the vegetables:
Blanch squash in salted boiling water until just tender. Remove and drain. Toss squash and mushrooms separately in melted butter.
For the tarragon foam:
Cook the tarragon and parsley in salted boiling water for 20 seconds, then immediately submerge them into an ice bath. Take the herbs from the ice bath and put them into a blender with 4 cups of water. Blend on high for a few minutes. Add the soy lecithin and puree. Pass the liquid through a fine-mesh strainer. Just before plating the dish, froth the juice in a blender until a foam forms.
Note: Fresh minced tarragon may be used in place of tarragon foam.
For the soft poached egg:
If you have a sous vide machine (immersion circulator), set it to 64°C (147°F) and cook the eggs in their shells in a water bath for one hour. Remove them and set aside until ready to plate.
At home, fill a skillet with 2 inches of water and a splash of white vinegar. Bring this to a simmer, then lower the heat. Crack the eggs into the water and poach them for 4 minutes. Remove them with a slotted spoon, taking care not to break the yolk.
Spoon the risotto into four bowls in equal portions. Place one poached egg into each bowl. Place a chicken thigh next to each egg. Spoon the glazed squash and mushrooms around the egg. Spoon bubbles of tarragon foam on top of each egg (or sprinkle the entire dish with minced tarragon). Finish with microgreens.