Combine the sifted whole wheat flour, sugar, spices, and salt in the center of a clean work surface or a 30 qt. standard weight mixing bowl. Make a well in the center of the flour mixture. Add the yeast and a little bit of the warm water and mix well until the yeast dissolves.
Add the beaten eggs to the wet mixture, followed by the melted butter. Begin to incorporate the flour, starting with the inner rim of the well. The dough will start to come together in a shaggy mass when about half of the flour is incorporated.
Continue kneading until smooth and elastic, about 15 minutes. You shouldn’t need to flour your surface, but lightly flour as needed if the dough sticks to it. Add the raisins, orange, and lemon zest to the dough and knead them until evenly distributed. Form the dough into a ball.
Generously butter a large clean bowl and transfer the dough ball to it. Turn the ball to coat with the butter, then cover the bowl with a clean kitchen towel. Let the dough rise in a warm place until doubled, about 1 to 1-½ hours.
Turn the dough out onto a clean work surface and divide it into 12 even pieces (about 90 to 100 grams each) with a bench scraper or sharp knife. Form each piece into a ball by folding it over itself and pulling the stretchy dough over the fruit bits, so they’re not sticking out.
Once you have a smooth ball, pinch the seam at the bottom shut and place the seam side down on the surface. Next, cup your hand over the ball and move your hand quickly in a circular motion to tighten the ball into a perfect round—place it in the prepared pan.
Repeat with the remaining dough and arrange the balls in a 3-by-4 grid, spacing evenly apart. Lightly brush each bun with oil. At this point, you can cover the pan tightly in plastic wrap and refrigerate it for up to 1 day. Next, cover the dough with a clean kitchen towel. Let the balls rise until their sides are touching, about about 1 to 1-½ hours (longer if the dough has been chilled).
Position a rack in the center of the oven and preheat to 350 degrees. In a small bowl, combine the flour, sugar, softened butter, and vanilla; slowly add milk to form a smooth paste, transfer to a pastry bag or zip-top bag and snip a ⅓-inch hole in one corner.
Pipe lines across the centers of the balls in one direction and then again in the opposite direction so that each ball has a cross. Bake the whole wheat hot cross buns until risen and browned, 25 to 30 minutes. The internal temperature of a center bun should register 190 degrees.
While the buns are baking, cook the apricot preserves and water in a medium pot over medium heat. Stir with a fork as it cooks until the mixture is a thin, shiny liquid, about 3 minutes. Remove from the heat. As soon as the buns come out of the oven, brush the syrup evenly over them. Serve Whole Wheat Hot Cross Buns hot, warm, or at room temperature.