Rinse the chicken breasts and pat dry with paper towels. Sprinkle with salt and pepper.
Melt the butter in a wide, heavy sauté pan over medium-high heat. Add the onion and sauté just until pale, about 5 minutes.
Add the pears and ginger, reduce the heat to medium, and shake and stir gently just until the pears are tender, 2 to 3 minutes. Scoop up the pears with a skimmer or slotted spoon and place in a bowl.
Return the pan to medium-high heat and add the chicken breasts, skin side down, to the fat remaining in the pan. Sauté, turning once, until well browned, 6 to 7 minutes on each side. Remove the chicken to a plate.
Add the cauliflower florets, arranging stems up. Raise the heat to high, add the stock, and bring to a boil. Cover, reduce the heat to low, and simmer the cauliflower until somewhat softened, about 5 minutes.
Remove the cauliflower with a slotted spoon and add to the bowl with the pears. Raise the heat and boil the juices until they darken and reduce to about 1/4 cup.
Return the chicken to the pan, top with the pears and cauliflower, and sprinkle with the ginger liqueur. Cover and simmer for 3 to 4 minutes longer.
Place the breasts on a platter with the sauce spooned over them.