Peel the pears, cut them in half lengthwise and, using a melon baller, scoop out the cores.
Rub them all over with the lemon half to prevent browning.
In a large (10-inch), heavy-based, ovenproof skillet, melt the butter.
Add the sugar and brown sugar and stir to dissolve.
Arrange the pears in the pan, cut side down, in a single layer.
Bake the pears uncovered, basting occasionally with the liquid in the pan, until they begin to soften and color slightly.
Depending on the pears ripeness, baking time can range from 20 minutes to 1 hour.
Remove the pears with a slotted spoon and set aside.
Transfer the pan to a burner and boil the mixture left behind over medium-high heat until it reaches a rich, golden-brown color and smells like caramel, 2 to 5 minute Slowly whisk the cream into the caramel until smooth.