For the Pickled Carrots: Using a mandoline, carefully slice the baby carrots 1/16 inch thick and place in a heatproof bowl. In a small saucepan, heat the extra virgin olive oil and sauté the onions until lightly browned. Add the garlic cloves, vinegar, black peppercorns, cumin, coriander seeds, bay leaf, salt, and sugar, and stir. Allow the mixture to simmer 5 minutes. Pour the warm vinegar mixture over the sliced carrots and let cool.
For the Mole Poblano: Preheat oven to 350°F. Line a baking sheet with nonstick aluminum foil. Cut the onion in half and place on the prepared baking sheet, cut-side down, along with the whole tomatoes. Roast about 30 minutes, rotating the vegetables every 10 minutes, until all the vegetables are cooked through and browned.
In a dry pan over medium-high heat, carefully toast the chilies and transfer to a bowl filled with warm water. Soak the chilies for 30 minutes to an hour, until they are soft.
In a sauté pan, add 1 tablespoon of the lard and, in separate batches, fry the almonds followed by the raisins. Set aside.
Remove the chilies from the water, and gently squeeze out some of the water. Place the chilies in a blender with 2 tablespoons water and purée until smooth.
Transfer the puréed chilies to a Dutch oven with the remaining lard and start cooking over medium heat.
In the blender, place the sesame seeds, coriander seeds, fried almonds, fried raisins, roasted white onion, garlic, brioche, tortillas, roasted tomatoes, whole cloves, freshly ground black pepper, anise seed, cinnamon stick, and 4 tablespoons of water. Blend until smooth. Add more water if necessary, but just enough to get the blades to move. Add the mixture to the Dutch oven with the chilies and cook down to a paste. Cook the mixture until reduced by about half, or until thick. Add the chocolate and season with salt and sugar. Cook for another 10 minutes and serve.
For the Roasted Carrots: Season the carrots with salt and toss in 1 cup mole. Place on a baking sheet, cover with foil, and bake for 40 minutes. Uncover and bake for another 20 minutes. Remove carrots from the oven and let them cool.
For the Mole Poblano Tuile: In a small saucepan, combine the Mole Poblano with 1 cup water and bring to a boil. Let the mixture cool slightly. Transfer to a blender, add the gellan gum, and blend on high speed. Add the sugar, dextrose, and a pinch of salt and blend until the mixture forms a gel. Continue blending until the gel becomes a smooth paste. Pass the paste through a fine-mesh sieve and spread thinly onto a silicone-mat-lined baking sheet. Place it in a dehydrator (or, alternatively, in the oven with only the pilot light on) and leave overnight to dry to a solid, thin sheet.
To Finish: Use a pastry brush to paint the inside of 4 deep bowls with Mole Poblano. To each bowl, add 2 ounces of Greek yogurt. Arrange 10 roasted carrots and sprinkle with 1 teaspoon sesame seeds followed by 6 sprigs of watercress. Arrange several slices of pickled carrots in each bowl and garnish with several artfully broken pieces of Mole Poblano Tuile.