Stir flour, salt, and sugar together. Cut in cold butter until pea-sized pieces remain. Drizzle in ice water and vinegar, mix just until clumpy. Divide dough, shape into two discs, wrap, and refrigerate at least 1 hour.

Toss sliced apples and pears with brown sugar, granulated sugar, cornstarch, cinnamon, nutmeg, and lemon juice until evenly coated.

Roll one dough disc into a 12-inch circle, line a 9-inch pie plate, trim overhang to 1/2 inch, and chill. Roll the second disc into a similar circle.

Spoon the fruit mixture into the chilled bottom crust, dot with the 2 tbsp cold butter. Place the top crust over the fruit, trim, fold edges under, and crimp to seal. Cut steam vents, brush with egg wash, and sprinkle with coarse sugar.

Place pie on a foil-lined baking sheet on the lowest oven rack. Bake at 400°F (200°C) for 20 minutes, then reduce to 375°F (190°C) and bake 30 to 35 minutes more, until crust is deeply golden and juices bubble thickly.

Cool the pie on a wire rack for at least 2 hours until the filling sets. Slice into wedges and serve slightly warm.