To make the gingerbread cake: Heat oven to 350 degrees. Butter a 8 3/4-by-4 1/4-by-2 3/4-inch loaf pan, and set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream butter and both sugars on medium speed until light and fluffy, 2 to 4 minutes. Add vanilla, and mix. Add eggs, one at a time, mixing well after each addition.
In a large bowl, sift together ginger, cinnamon, nutmeg, cloves, baking soda, baking powder, salt, and flour. Gradually add flour mixture to the butter mixture, and mix on low speed just until the flour has been incorporated. Pour batter into prepared pan, and smooth the top with a spatula.
Bake until a cake tester inserted into the middle comes out clean, 50 to 55 minutes. Transfer to a wire rack to cool completely. Run a knife between the cake and the pan, and invert onto a serving platter.
Using a paring knife, make a trough in the center of the cake: Insert knife halfway into the cake, and cut a rectangle, leaving a 3/4-inch border all around. Insert a serrated knife through one long side of the cake, intersecting the cut made by the paring knife through the top. Cut bottom of the trough, being careful not to cut through the shorter sides or all the way through the cake. Lift out trough, and reserve for snacking. Cover cake with plastic until ready to assemble.
To make the poached pears: Peel pears, and place in a medium saucepan. Add remaining ingredients and just enough water to cover pears.
Set saucepan over high heat, and bring to a boil. Reduce to a simmer, and cook, stirring gently, over medium-low heat until a paring knife easily pierces pears, about 15 minutes. Remove pan from heat; let pears cool in liquid.
Using a slotted spoon, transfer pears to a plate. Pour poaching liquid through a sieve set over a bowl. Discard solids, and return liquid to saucepan. Place over medium-high heat, and cook until liquid has been reduced to a syrup that coats the back of a wooden spoon, about 45 minutes. Let cool; store pears in red-wine syrup in an airtight container until ready to assemble dessert.
To make the cinnamon cream: Place heavy cream, sugar, and cinnamon in a chilled medium bowl. Using a whisk, whip cream until soft peaks form. Cover with plastic, and refrigerate until ready to use.
To assemble dessert: Slice poached pears in half, and remove the cores with a melon baller. Unwrap cake, and dust with confectioners' sugar. Stand halved pears in the trough of the cake. Drizzle 2 tablespoons red-wine syrup over the tops. Serve cake with additional syrup, and dollop each portion with cinnamon whipped cream.