Heat 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 oven and rub warm toast with halved garlic clove, season with sea salt and top with a little parsley, reserving some of the parsley for garnish.
Place onions in a small skillet with 1/2 cup chicken stock and a pat of butter. Sprinkle with sugar, bring to simmer then let the onions reduce until liquid evaporates and 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 chicken with salt and pepper and add to pan, brown 2-3 minutes per side then remove the chicken to a plate. Add chopped onions, carrot, chopped garlic, bay and thyme, and stir 2-3 minutes to soften. Add bacon back to pan with the wine and about 1 cup stock. Add dark meat back to skillet and simmer at low rolling bubble 8-10 minutes, turning occasionally. Add white meat and simmer 6-8 minutes more, turning occasionally. Stir in potato starch to thicken then remove from heat.
Meanwhile, in small skillet over medium to medium-high heat, melt 2 tablespoons butter. Add mushrooms and brown 4-5 minutes, season with a little salt and pepper, toss with parsley.
To serve, line a shallow bowl with crispy toasts and top with 1 small breast and 1 piece of dark meat, pearl onions and mushrooms.