1. In a large pot, place the pears, sugar, lemons, and vanilla. Fill with water to cover. Cover and bring to a boil. Reduce heat to medium and cook the pears just until tender but not soft, about 30 minutes. Test the pears for doneness by carefully piercing them with a paring knife. The knife should slip in and out without pulling apart the fruit. Remove the pears with a slotted spoon and drain, upright, on paper towels. Do not discard the cooking water.
2. When the pears are cool enough to handle, slice off the top third and set aside. With a small scoop or melon baller, carefully remove the cores and seeds, keeping the pears whole.
3. Preheat the oven to 300 F.
4. Place the pears upright in a glass baking dish and pour 2 cups of the reserved cooking liquid around them. Fill the pear centers with the Crème Brûlée.
5. Bake in the lower third of the oven until the crème brûlée mixture has set and turns golden, about 1 hour and 15 minutes. Check the mixture by lightly squeezing the pears.
6. Remove the pears from the oven and sprinkle with the brown sugar.
7. Preheat the broiler.
8. Place the pears under the broiler until sugar melts and bubbles, about 1 minute. Set aside to cool.
9. To serve, drizzle 2 tablespoons of the Crème Anglaise and the Raspberry Coulis over each of 10 dessert plates. Place a pear in the center of each plate and replace the pear tops. Garnish the edges of each plate with 3 fresh raspberries and a sprig of mint. Set aside to cool for 20 minutes before serving.
Note: The pears can be made in advance and refrigerated. To serve, sprinkle the pears with a little brown sugar and heat briefly under a hot broiler, just to melt the sugar.