Prepare the Pastry Dough:

In a large bowl, whisk together flour, sugar, and salt. Add cold cubed butter and work it into the flour until the mixture resembles coarse crumbs with some pea-sized pieces. Drizzle ice water and vanilla extract over the mixture, stirring gently until dough forms. Shape into a disk, wrap in plastic, and refrigerate for at least 1 hour.

Create the Almond Cream:

Beat softened butter and sugar until light and fluffy. Add egg, vanilla, and almond extracts, mixing well. Fold in almond flour, all-purpose flour, and salt until smooth. Cover and refrigerate until ready.

Prepare the Banana Filling:

Slice bananas into ¼-inch rounds. Toss with brown sugar, lemon juice, and cinnamon. Let sit 5-10 minutes to meld flavors.

Assemble the Galette:

Preheat oven to 375°F (190°C). Roll chilled dough into a 12-inch circle on a floured surface. Transfer to a parchment-lined baking sheet. Spread almond cream evenly over the center, leaving a 2-inch border. Arrange banana slices on top in overlapping layers.

Fold and Bake:

Fold dough edges over filling, pleating as needed. Brush dough with egg wash, sprinkle sliced almonds and turbinado sugar. Bake 35-40 minutes until crust is golden and filling bubbles. Tent with foil if browning too fast.

Finish and Serve:

Cool for at least 15 minutes. Optionally brush with warmed apricot jam for shine. Serve warm or at room temperature.