Activate the yeast. Combine the warm (not hot) milk with the yeast, 2 tbsp sugar and 1 tbsp flour, taking the sugar and flour from the measured recipe totals. Cover and leave in a warm place for 20–30 minutes, until the mixture looks bubbly.
Prepare the remaining ingredients. Finely grate the carrots and zest the mandarin or orange and half a lemon. Have the softened butter, eggs, remaining sugar and flour, salt and vanilla ready. Brush the inside of the Bundt pan with vegetable oil, including the center tube and grooves.
Mix the dough. In a large bowl, mix the softened butter with the remaining sugar, then mix in the eggs, vanilla and citrus zest. Add the grated carrots and the yeast mixture. Gradually mix in the remaining flour and salt until evenly combined and no dry flour remains.
Fill the pan and let rise. Transfer the dough to the greased Bundt pan and spread it evenly around the center tube. Cover and leave in a warm place for about 1 hour, or until doubled in size. Allow enough room in the pan for the dough to expand.
Bake and serve. Toward the end of the rise, preheat the oven to 180°C / 350°F. Remove the cover and bake for about 40 minutes, until a toothpick inserted into the thickest part comes out clean. Let the cake cool enough to release from the pan, turn it out carefully and let it cool before dusting with powdered sugar. Slice and serve with tea and a little butter, if desired.
