For the Pears: Peel the pears if desired. Cut the pears in half and scoop out the cores. Cut each half in half again.
Arrange the pear pieces cut-side down in a large saute pan. Dot the butter all around the pears and place the pan over medium heat. Cook, occasionally swirling the pan but not stirring, until the pears are lightly browned and the butter begins to sizzle, 3 to 5 minutes.
Sprinkle the cinnamon and fennel seeds over the pears, then gently stir and baste the pears with the butter and spices. Continue to cook just until the pears are tender, then add the vanilla and gently stir to incorporate. Keep the pears warm until ready to serve.
For the Caramel Sauce: Stir together the granulated sugar, lemon juice and 2 tablespoons water in a heavy-bottomed saucepan. Place the pan over medium heat, swirling the mixture occasionally (do not stir). If you notice crystals forming around the edge of the pan, wipe the inside of the pot with a pastry brush moistened with water.
Cook the sugar mixture at a simmer until it has turned deep brown and registers between 330 and 350°F on a candy thermometer, about 10 minutes. Remove the pot from the heat and stir in the butter, salt and pepper until completely incorporated. Carefully add the heavy cream. Reserve warm, or refrigerate until ready to serve. (Keeps up to 4 weeks, refrigerated in an airtight container.)
For the Whipped Creme Fraiche: In a clean bowl, beat together the heavy cream, creme fraiche, confectioners' sugar and vanilla extract with an electric mixer or by hand until stiff peaks form. Reserve chilled until ready to serve.
Arrange the pears on a platter. Drizzle with 1/2 cup of the caramel sauce, then top with a couple dollops of the whipped creme fraiche. Serve with additional caramel sauce and whipped creme fraiche on the side.