Add the water, teaspoon of sugar, and yeast to the bowl of a stand mixer, and stir until combined. Let the mixture sit for 5 minutes, or until it becomes foamy.
Add the flour, salt, mixed spice, sugar, butter, and egg, and turn the mixer on low. As the ingredients come together, gradually add the milk until a smooth, elastic dough forms that pulls away from the sides of the bowl. You may use all of the milk or a partial amount. It just depends on how much liquid your flour absorbs.
Once you have a smooth, elastic dough, let the dough continue to mix on medium speed for 7-10 minutes, or until it can pass the windowpane test, which is where you stretch a small piece of dough, and if it doesn't break and you can see light through it, the gluten has properly developed. Remove your kneaded dough from the mixer and work in the dried fruit and candied peel by hand until fully incorporated.
Transfer your dough to a large bowl and cover it with plastic wrap. Let the dough rise in a warm place until doubled in size, about 1 to 1½ hours. Enriched doughs with dried fruit tend to rise slowly.
Once doubled in size, punch down the dough and divide it into 12 equal portions. An easy way to do this is to weigh the dough in grams and then divide that number by 12. Each ball of dough should weigh roughly that amount.
Form each portion of dough into buns by pulling in all the edges towards the center and then pinching the dough together. Turn the ball of dough over and roll it in a circular motion under the palm of your hand on an un-floured surface to help create tension and seal the bottom. Place each formed bun in a 3 x 4 pattern in a 9"x13" (23x33 cm) pan or a quarter sheet pan. Cover them with plastic wrap and let them rise for 30 minutes to 1 hour, or until doubled in size.
Once doubled, preheat your oven to 425℉ / 220℃ and mix together a flour-water paste using all-purpose flour and water. You want the paste to be thick enough to squeeze through a piping bag in a line. Once you've reached the right consistency, scoop the paste into a piping bag or a makeshift piping bag using a small resealable plastic bag. Snip off the end of the bag just wide enough to be able to squeeze the paste out in a thin line.
Squeeze the paste across the top of each bun to form a cross that reaches from one side of the bun to the other. Bake them in the pre-heated oven for 12-15 minutes, or until golden brown.
Remove the buns from the oven and gently heat the strained apricot jam in the microwave. Brush it across the top of the buns for a sweet and shiny glaze. Serve the buns warm or at room temperature.