In a large mixing bowl, whisk together the flour, sugar, yeast, and salt. Make a well in the center.
In a small bowl, whisk together the milk, butter, egg, and vanilla extract, then add to the center of the bowl. Use a wooden spoon to stir everything together. The dough will be sticky, but should come together. Add more flour a tablespoon at a time if needed.
Turn the dough out onto a floured work surface and knead until smooth and elastic, about 5 minutes.
Place into an oiled bowl, cover with plastic wrap, and allow to rise until doubled in size, about 1 hour.
With the dough still in the bowl, add the raisins, orange zest, cinnamon, cloves, and nutmeg. With your hands, knead everything into the dough, making sure it is well distributed. Cover the bowl and allow to rise again until doubled in size, another 1 hour.
Turn the dough out onto a work surface and divide into 15 even pieces. Roll each piece into a smooth ball and place at least 1 ½ inches apart on a half sheet pan that has been lined with parchment paper or a silicone baking mat. Cover loosely with plastic wrap and allow to rise until the rolls are puffed, about 1 hour.
Preheat oven to 425 degrees F.
Make the Cross Paste: In a small bowl, stir together the flour and 5 tablespoons of water. Add the water 1 tablespoon at a time; use only enough to make a very thick paste. Spoon the paste into a piping bag or resealable plastic bag and snip off the end. Pipe the paste down and across each row to make a cross on top of each roll.
Bake until golden brown and the internal temperature registers 195 degrees F, about 15 to 20 minutes.
Prepare the Glaze: Heat the jam in a small saucepan over low heat or, alternatively, in the microwave in 30-second bursts until melted. Strain through a fine-mesh sieve to remove chunks, then brush over warm hot cross buns.
Serve buns warm or at room temperature.