Pour chicken stock into a pan wide enough to accommodate the pears; bring to a gentle boil.
Peel pears, slice in half lengthwise, and core.
Poach pear halves in simmering stock 2 to 3 minutes, covered, until just tender.
Remove pears and set them aside.
Boil chicken stock rapidly until reduced to 1 cup.
Set stock aside.
Preheat oven to 350 degrees.
Pound fillets to flatten slightly.
Melt 2 to 3 tablespoons butter in a large frying pan over medium-high heat.
Saute fillets, 6 to 8 at a time, 2 minutes on each side, until lightly browned.
When browned, place fillets in a large, shallow baking dish.
Replenish the butter in the pan as needed to finish sauteeing the pork.
Season fillets with salt and pepper.
When all meat is browned, prepare a thin sauce by sauteeing shallots over medium heat in the same frying pan, adding additional butter if necessary.
Cook shallots 2 or 3 minutes, until soft.
Pour into the pan the reduced chicken stock and simmer sauce 1 or 2 minutes, scraping the pan as you stir.
Keep warm.
Fill poached pears with equal portions of blue cheese, then place them on top of the sauteed pork fillets.
Bake at 350 degrees 15 to 20 minutes, or until cheese melts and meat is cooked through.
When meat is done, pour the shallots and chicken stock over it.