Prepare dry ingredients: Sift the cake flour, whole wheat flour, and salt together.
Mix wet ingredients: In a bowl, whisk together sugar, soy milk, and coconut oil quickly.
Make dough: Add the wet mixture to the sifted dry ingredients and stir with a spatula. Form the mixture into a ball, wrap it in baking paper, and rest in the fridge for 10 to 15 minutes.
Prepare tomato filling: Remove stems from washed tomatoes and dice them.
Cook tomatoes: Add diced tomatoes and light brown sugar to a pan. Boil down over medium heat for about 8 minutes. Add white balsamic vinegar at the end and stir. Cool slightly, then refrigerate until completely cooled.
Assemble tart: Roll out the dough thinly with dusted flour. Sprinkle a thin layer of dark brown sugar on the dough. Arrange the cooled tomato mixture on top, removing as much moisture as possible. Fold the edges of the dough inward.
Add finishing touches: Spread some of the boiled-down tomato syrup around the edge of the tart. Sprinkle with light brown sugar and dark brown sugar. Optionally, add rosemary or thyme for extra aroma.
Bake: Preheat oven to 180°C (356°F). Bake the tart for 50 minutes until golden and cooked through.