Preheat the oven to 375 degrees F (190 degrees C).
Combine flour, salt, baking powder, and sugar in a bowl. Whisk until thoroughly combined. Grate in the frozen butter, stopping occasionally to toss the butter into the flour mixture until coated. Drizzle in vanilla extract; add egg yolks. Stir with a fork until egg is mostly absorbed. Add vinegar; mix briefly. Use your hands to finish mixing, squeezing until clumps but mixture remains mostly dry. Add 1 teaspoon vinegar if needed.
Combine blueberries, raspberries, and blackberries in another bowl. Add lemon zest, lemon juice, sugar, and cornstarch. Sprinkle in cayenne pepper. Mix until sugar and cornstarch are mostly dissolved.
Place about 1/2 of the crumble mixture into the bottom of a 2-quart baking dish. Press mixture down using a flat cup until well compacted. Spread the berries over the crust. Sprinkle the remaining crumble mixture on top, squeezing some of it into clumps.
Bake in the preheated oven until top is beautifully browned and berry syrup bubbles on the surface, 40 to 45 minutes. Let cool to room temperature, about 30 minutes.