Creating the Pink Grapefruit Valentine Galette is simple when you follow these steps:

1. Prepare the Dough: In a large bowl, mix the flour, salt, and sugar. Add the cubed butter and mix with your fingers or a pastry cutter until it resembles coarse crumbs.
2. Add Ice Water: Gradually add ice water, one tablespoon at a time, mixing until the dough forms a ball. Flatten into a disc, wrap in plastic wrap, and refrigerate for at least 30 minutes.
3. Prepare the Filling: In a bowl, combine the grapefruit segments, juice, sugar, cornstarch, and vanilla extract. Toss gently to coat the grapefruit evenly.
4. Preheat the Oven: Preheat your oven to 375°F (190°C) while you roll out the dough.
5. Roll Out the Dough: On a lightly floured surface, roll the chilled dough into a 12-inch circle. Transfer it to a parchment-lined baking sheet.
6. Add the Filling: Spoon the grapefruit mixture into the center of the dough, leaving a 2-inch border around the edges.
7. Fold the Edges: Fold the edges of the dough over the filling, pleating as necessary to create a rustic edge.
8. Apply Egg Wash: Brush the folded dough with the beaten egg and sprinkle with coarse sugar, if desired.
9. Bake: Bake for 35-40 minutes, or until the crust is golden brown and the filling is bubbly.
10. Cool: Remove from the oven and let cool on a wire rack for 10-15 minutes before serving.

These steps will guide you in creating a stunning Pink Grapefruit Valentine Galette that is sure to impress!