For the cake: Preheat the oven to 350 degrees F. Line a rimmed baking sheet with parchment and spray with baking spray.
Sift together the flour, cornstarch, baking soda and salt in a bowl.
In the bowl of an electric mixer fitted with a paddle attachment, cream the granulated sugar and butter until light and fluffy, 2 to 3 minutes. Add the eggs one at a time, mixing well after each addition. Add the sour cream and vanilla and mix until combined. Add the sifted dry ingredients and mix on low speed until just barely combined.
Pour into the prepared baking sheet and bake until the cake is golden and a toothpick inserted in the center comes out clean, 30 to 35 minutes. Set aside and allow to cool completely.
For the strawberries in sauce: Put the granulated sugar, cornstarch, gelatin and 1 1/2 cups water in a saucepan. Stir together and bring to a boil. Cook until starting to thicken, then remove from the heat. Put the strawberries in a bowl and pour over the sauce, gently tossing together. Set aside in the fridge and allow the mixture to thicken, stirring occasionally, 10 to 15 minutes.
For the sweet yogurt cream: In the bowl of an electric mixer fitted with the whisk attachment, whip the yogurt, cream, granulated sugar and brown sugar on high until smooth and silky.
Once the cake is cool, flip out onto a cutting board and remove the parchment. Cut the cake into 1.5-inch cubes.
To assemble the trifle, place half of the cake pieces into the bottom of a trifle dish or large glass bowl. Top with half of the strawberries in sauce, then half of the sweet yogurt cream. Repeat the layers of cake, strawberries in sauce and cream. Garnish with fresh halved strawberries and mint leaves. Cover and place in the refrigerator to chill for at least 2 hours.