Combine the rhubarb, strawberries, sugar, lemon juice, cornstarch, vanilla, and salt in a small saucepan, then cook over medium heat, stirring often, until the fruit releases liquid, the rhubarb softens, and the mixture thickens into a jammy compote, 8 to 12 minutes. The filling is ready when the rhubarb is tender but still has some small visible pieces, the strawberries have mostly broken down, and a spatula dragged across the pan leaves a line for 1 to 2 seconds before slowly closing back in. Don't leave the filling loose or watery, or it will flood the cookies once baked. Transfer to a shallow bowl or plate, cool completely, then refrigerate until cold and thick, about 30 to 40 minutes.

Mix the flour, oats, brown sugar, cinnamon, and salt in a medium bowl, then pour in the melted butter and mix with a fork until small clumps form. You want irregular crumbs, not a paste. Refrigerate until needed so the topping stays crumbly rather than softening.

Beat the softened butter, light brown sugar, and granulated sugar together until creamy and smooth, 2 to 3 minutes, then add the egg, egg yolk, and vanilla, mixing until fully incorporated. Whisk together the flour, oats, cornstarch, baking soda, baking powder, and salt in a separate bowl, then add the dry ingredients to the butter mixture and mix just until no dry flour remains. The dough should be soft, thick, and slightly tacky. Don't overmix once the flour is in, or the cookies can become tougher and spread less evenly.

Cover and refrigerate the dough for 30 minutes, until firm enough to scoop cleanly. This chilling step matters for thick cookies and helps control spread once the fruit filling is added.

Line baking sheets with parchment, then scoop the dough into 24 portions, about 40–45 g each, flattening each slightly in your hand or on the tray. Add about 2 teaspoons of the cold strawberry-rhubarb filling to the center of each, then fold or mound the dough loosely around the filling so it's mostly enclosed but with a little filling still peeking through for the rustic oat crisp look. Top each cookie with a generous spoonful of the chilled oat crisp topping, pressing very lightly so it adheres without flattening the cookie too much. Refrigerate or freeze the tray for 15 to 20 minutes before baking if the dough softens while shaping, which helps especially in a warm kitchen.

Heat the oven to 180°C conventional / 170°C fan. Bake 6 cookies at a time per tray, leaving enough space between them, for 14 to 16 minutes, until the edges are deep golden brown, the oat topping is set and lightly toasted, the centers are puffed and mostly set, and the fruit filling is bubbling in spots. Don't overbake — the centers should still look a little soft when you pull them, since they finish setting on the hot tray.

Let the cookies cool on the baking sheet for 15 minutes before moving them, since the fruit filling is very soft when hot and needs this rest to thicken and set inside the cookies. Transfer carefully to a rack and cool completely, or serve slightly warm.