Step 1: In a large bowl, whisk together the flour, salt, and granulated sugar. Cut in the cold butter using a pastry cutter until the mixture resembles coarse crumbs.
Step 2: Gradually add ice water, one tablespoon at a time, mixing until the dough just begins to come together. Form into a disc, wrap in plastic, and refrigerate for at least 1 hour.
Step 3: Preheat your oven to 400°F (200°C). Toss sliced apples with honey, lemon juice, and half of the chopped sage leaves. Spread on a baking sheet and roast for 10 minutes to soften slightly.
Step 4: On a floured surface, roll out the chilled dough into a 12-inch circle. Transfer to a parchment-lined baking sheet.
Step 5: Arrange the roasted apples in the center of the dough, leaving a 2-inch border. Scatter the remaining whole sage leaves over the apples.
Step 6: Fold the edges of the dough over the apples, pleating as you go. Brush the crust with the beaten egg and sprinkle with coarse sugar.
Step 7: Bake for 30-35 minutes, or until the crust is deeply golden and the apples are bubbling. Let cool slightly before slicing your roasted apple and sage galette.