Pre-heat the oven to 350°F.
Brush the baguette slices with olive oil on both sides and arrange on a metal rack set on a rimmed baking sheet and toast until evenly golden, 12-15 minutes. Remove from the oven and rub the warm toast with the halved garlic clove; season with sea salt and top with a little parsley, reserving some of the parsley for garnish.
Place the pearl onions in a small skillet with 1/2 cup chicken stock and a pat of butter. Sprinkle with sugar and bring to simmer, then let the onions reduce until the liquid evaporates and the onions brown; cover and reserve.
Heat a large, cast iron skillet or other heavy pan over medium to medium-high heat with about 1 tablespoon of olive oil, a turn of the pan. Add the bacon and crisp; remove. Season the chicken with salt and pepper and add to the pan; brown for 2-3 minutes per side, then remove the chicken to a plate. Add the chopped onion, carrot, chopped garlic, bay and thyme and stir for 2-3 minutes to soften. Add the bacon back to the pan with the wine and about 1 cup stock. Add the dark meat back to skillet and simmer at a low rolling bubble, 8-10 minutes, turning occasionally. Add the white meat and simmer for 6-8 minutes more, turning occasionally. Stir in the potato starch to thicken, then remove from the heat.
Meanwhile, in small skillet over medium to medium-high heat, melt the remaining 2 tablespoons butter. Add the mushrooms and brown for 4-5 minutes; season with a little salt and pepper and toss with parsley.
To serve, line a shallow bowl with crispy toasts and top with one small breast and one piece of dark meat, the pearl onions and mushrooms.