To poach the pears, bring 4 cups water to a boil in a medium saucepan. Remove from the heat and add the ginger and black tea bags; let steep 10 minutes. Squeeze the bags against the side of the pan, then discard them. Stir in the sugar, honey, peppercorns, ginger and lemon peel and bring to a simmer. Add the pears and additional water to cover the pears, if needed. Simmer, turning the pears occasionally, until just tender all the way through, 20 to 22 minutes. Let cool in the liquid. Halve and core the pears and pat dry. Slice the pears into 1/4-inch slices. (You'll get 6 or 7 slices from each pear.)
Heat the butter in a medium skillet over medium heat. Add the leeks and cook, stirring occasionally, until tender, about 10 minutes. Season with salt and pepper. Set aside to cool.
Preheat the oven to 400 degrees F.
Unroll the pie crust on a floured work surface and roll to a 14-inch circle. Center on a parchment-lined baking sheet (it's OK if it overhangs at this point). Spread the leeks on the crust in a 9-inch circle. Sprinkle the cheese over the top. Top with the pears in a spiral. Fold over and pleat the edges of the dough, leaving the center of the galette open. Brush the dough with the beaten egg.
Bake the galette until the juices are bubbling and the pastry is golden brown and crisp, 40 to 45 minutes. Remove to a baking rack to cool. Serve warm or at room temperature, sprinkled with the chives, if using.