Rub the finely minced lemon zest into the 4.2 oz of sugar using your fingertips, pressing gently to release the oils and create a fragrant lemon sugar. This infuses the sugar with bright citrus flavor that will permeate throughout the dough. While the zest releases its oils, measure out all remaining dry ingredients (bread flour, yeast, salt) and the wet ingredients (room temperature milk, egg, vanilla extract) into separate bowls for quick incorporation.
Combine the dry ingredients (bread flour, yeast, salt, and lemon sugar from Step 1) in a large bowl. Create a well in the center and pour in the milk, egg, and vanilla extract from Step 1, then add the diced citrus peel and 3 tbsp poppy seeds. Mix by hand until a shaggy dough forms, then add the butter in small pieces and knead on medium speed (using a stand mixer) for 10 minutes until the dough becomes smooth and elastic. I like to let the mixer do the work here rather than hand-kneading—it develops the gluten more evenly for a better rise.
Shape the dough from Step 2 into a smooth ball and place it in a lightly oiled bowl or covered container. Cover loosely with plastic wrap or a damp towel and let it rise in a warm spot (around 75-80°F) for 1 to 1.5 hours, until roughly doubled in size. You can use your oven with the light on, a proofing box, or any warm corner of your kitchen.
Preheat your oven to 180°C (350°F) and line a baking tray with parchment paper. Turn out the risen dough from Step 3 onto a lightly floured surface and gently flatten it. Divide the dough into 12 equal pieces (I find it helpful to cut it into quarters first, then divide each quarter into three pieces for consistency). Roll each piece between your palms into a smooth, tight ball and place seam-side down on the prepared tray, spacing them about 1.5 inches apart to allow room for rising.
Cover the shaped buns loosely with plastic wrap and let them rise for 45 minutes at room temperature until puffy and touching slightly. While the buns rise, mix the 2.6 oz flour with the 2.5 fl oz water in a small bowl, stirring until you have a smooth, pipeable paste. The paste should be thin enough to pipe through a narrow tip but thick enough to hold its shape on the buns.
Once the buns have risen, pipe the cross paste from Step 5 onto each bun in two thin, perpendicular lines using a small piping bag or squeeze bottle. Bake in the preheated 180°C oven for 22 to 25 minutes until the buns are golden brown and the crosses are set. The buns should sound hollow when tapped on the bottom when done.
While the buns bake, combine the 2.6 fl oz of freshly squeezed lemon juice with the 1.6 oz of sugar in a small saucepan and bring to a boil, stirring gently for about 1 minute until the sugar dissolves completely. The syrup will thicken slightly as it cools. Remove the hot buns from the oven and immediately brush the warm lemon syrup over each bun, then sprinkle with poppy seeds and small pieces of candied lemon peel for garnish. Serve the buns warm or at room temperature.