Make-Ahead: The shortcakes can be prepared up to 8 hours before serving, cooled completely and wrapped in aluminum foil. Reheat the foil-wrapped biscuits in a preheated 350°F oven for 10 minutes before using.) The pears can be peeled and prepared 2 hours before serving, covered, and refrigerated.
2. On a lightly floured work surface, roll out to 1/2-inch thickness. Using a 3-inch diameter star-shaped biscuit cutter, cut out biscuits. Gather up the scraps, knead lightly, reroll and cut out additional biscuits to make a total of 24. Place on two ungreased baking sheets, spacing 2 inches apart. Brush the tops of the biscuits lightly with the egg, then sprinkle with the remaining 1 teaspoon of sugar.
3. Bake until golden brown, switching the positions of the racks from top to bottom and front to back halfway through baking, 18 to 20 minutes. (The biscuits can be prepared up to 8 hours before serving, cooled completely and wrapped in aluminum foil. Reheat the foil-wrapped biscuits in a preheated 350° F oven for 10 minutes before using.)
4. To make the filling: In a medium bowl, toss the pears with the lemon juice. (The pears can be prepared up to 2 hours ahead, covered, and refrigerate.)
5. In a very large skillet, melt the butter over medium heat. Add the pears and cook, stirring occasionally, until just tender, about 6 minutes. Stir in brandy, then brown sugar.
Add heavy cream, increase the heat to high, and bring to a boil. Cook until cream reduces by about one-third (it should coat a wooden spoon), about 5 minutes. 6. To serve, divide the hot pears into 12 shallow bowls. Top each serving with 2 biscuits, garnish with mint sprigs and raspberries, and serve warm.