Preheat and prep. Preheat the oven to 350°F (180°C). Generously butter the bottom and sides of a 10-inch (26 cm) springform pan that is at least 3 inches (7.5 cm) deep. Toss the strawberry halves with 2 tablespoons of flour or semolina until lightly coated and 1 spoon of sugar, then set aside.
Mix the base by hand. In a large bowl, whisk the mascarpone, softened butter and sugar vigorously until pale, creamy and smooth. You can use a spoon at this stage.
Add the eggs one by one or all at once and whisk until combined. If you are using clear vanilla extract or vanilla sugar, whisk it in now.
Add the flour in batches, along with the almond flour, baking powder and salt. Switch periodically between a whisk and a spoon or spatula, as you will need both to work through the thick batter. Fold gently just until the flour streaks disappear. The final batter should be thick but spoonable, keeping in mind you may need slightly more or less flour depending on the type you use. Do not overmix.
Pour half of the plain batter into the pan and spread it evenly.
Stir the cocoa with the cold milk into a smooth, lump-free paste. Fold it and the dark vanilla into the remaining batter, adding chocolate chips if you like.
Create the marble swirl. Spoon the chocolate batter over the vanilla layer and drag a butter knife through both in a zig-zag pattern.
Add the strawberries. Arrange the coated strawberries cut-side down over the batter and press them in very slightly.
Bake for 45 to 60 minutes, checking at 45. Strawberries release moisture, so timing depends on your oven. Near the end, you can switch on the fan (convection) briefly to cook off extra fruit moisture. The cake is done when a toothpick in the center comes out clean. Cool in the pan for 10 minutes, release the ring and dust with powdered sugar. Serve warm or at room temperature.