Pulse egg yolks, both flours, baking powder, salt, and granulated sugar in a food processor to combine. Add butter and pulse until only pea-size pieces remain. Drizzle in ⅔ cup cream, then pulse 2–3 times to barely incorporate. Transfer dough to a work surface and gently fold on top of itself several times just to bring it together and work in any dry spots.
Using a 2-oz. ice cream scoop, make 6 balls and place on a parchment-lined baking sheet. Do not flatten. (Or measure out mounded scoops with a ¼-cup measuring cup.) Cover and chill until cold, 20–25 minutes.
Preheat oven to 350°. Brush tops of shortcakes with remaining 2 Tbsp. cream and sprinkle with sanding sugar. Bake until golden and sides are firm to the touch, 28–32 minutes. Let cool.
Toss strawberries, granulated sugar, lemon zest, and a pinch of salt in a medium bowl to combine. Transfer half of strawberries to a large saucepan and add 1 Tbsp. water; let remaining strawberries macerate while you bring strawberries in saucepan to a gentle simmer over medium-low. Cook, stirring occasionally and reducing heat if needed to keep at a low simmer, until strawberries are starting to break down and become jammy and liquid is syrupy, 12–18 minutes. Let cool, then stir in 1 tsp. lemon juice. Stir remaining 1 tsp. lemon juice into macerated strawberries.
Combine heavy cream, powdered sugar, and a pinch of salt in a medium bowl. Scrape in seeds from vanilla bean; reserve pod for another use. Beat cream until soft peaks form.
Split shortcakes and divide strawberry compote, macerated strawberries, and whipped cream among bottoms. Close with shortcake tops.
Do Ahead: Shortcakes can be baked 1 day ahead. Store airtight at room temperature. Reheat before serving.