To build the levain: In a tall jar or medium bowl, mix the mature starter, flours, and warm water until incorporated. Cover with a lid or clean kitchen towel and leave in a warm place for
3 to 4 hours. You can use your levain immediately, or refrigerate it for 12 hours to use later or the next day.
To make the final dough mix: In a large bowl, whisk the eggs and cold milk to combine. Add the levain, brown sugar, lemon zest, and vanilla. Whisk until just incorporated. Add the cubed butter, flours, and salt. Using your hands, squeeze everything together and then turn the dough out onto a work surface. Knead the dough using the palm of your hand to push it forward, and then your fingers to pull it back toward your hand. Repeat this process until you have a smooth surface. Don't be afraid to rip this dough while you knead with your palm and then bring it back together again. Cover the dough and let ferment at room temperature for 6 hours. Refrigerate the dough for 12 hours more.
To shape, fill, and proof the dough: Line a sheet pan with parchment paper and set aside. Turn the dough out on to a floured work surface and pat it down and into a rectangle about 12 x 8 inches (30 x 20 cm). From the filling ingredients, spread the room-temperature butter over the dough and evenly sprinkle the granulated sugar on top. Cut the rectangle horizontally into 12 (1-inch-, or 2.5 cm, wide) strips. Roll each strip into a pinwheel. Arrange the mallorca rolls on the prepared sheet pan with enough space between so they can grow. It’s also okay if they touch during the bake. Fill an ovenproof pot with boiling water and put it into the cold oven. With the oven off and cold, put your trays of mallorcas inside the oven and let them proof for 2 to 3 hours.
To bake the mallorcas: Remove the mallorcas and pot from the oven. Preheat the oven to 375°F (190°C). Using a pastry brush, brush the tops of the mallorcas with water. Bake the mallorcas for 20 minutes, or until light brown. Sprinkle liberally with powdered sugar while warm.