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heat a medium skillet with the butter over medium heat.
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add the peaches and the juice of 1/2 lemon, and cook until tender and lightly golden, 10 minutes.
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turn off the heat.
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while the peaches cook, heat 1 tablespoon olive oil in a large skillet over medium-high to high heat.
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add the chicken breasts or thighs to the pan and season with salt and pepper, to taste.
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cook until the chicken is cooked through, about 12 minutes, then remove to a plate and cover with foil.
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drizzle the pan with the remaining olive oil.
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add the chopped shallot, and the ginger, and cook for 1 to 2 minutes.
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stir in the stock, the preserves, hot sauce and worcestershire sauce and season with salt & pepper, to taste.
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cook over medium heat for a couple of minutes to thicken.
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arrange the chicken and peaches on a platter and pour over the peach sauce.