Make the dough:

• Sprinkle the yeast on the warm water in a small bowl with a pinch of the
  sugar. Set aside for about 5 minutes until the yeast is foamy.
• Warm the butter, milk, salt, and the rest of the sugar in a small pan on
  the stove until you see bubbles around the edges.  Stir to finish melting the butter.
• Crack your eggs into a wide shallow dish, like a pie plate.
• Use a fork to whip the eggs into the butter and milk mixture, then add in half the lime zest.
• Check the temperature with
  your finger (the milk/egg mixture should be just warm to the touch.).
• Put the flour into a large bowl or your stand mixer bowl. Make a well in
  the center with your hands, then pour in the milk mixture then the yeast
  mixture. Stir with a wooden spoon to make a rough dough.
• After that, with a dough hook on your stand mixer, beat the dough for
  about 5 minutes on low speed (2 on a Kitchen Aid) until you get an elastic
  sticky dough that pulls away in strands from the sides of the bowl.
• Cover the dough with plastic wrap and set in the fridge to rise
  overnight or 4 hours minimum.

Assemble the rolls

• Sprinkle some flour on a work surface, then scrape out the cold dough on
  top of the flour. Sprinkle flour over the top of the dough.
• Quickly roll the dough into a rectangle about 12″X16″.
• Line two half sheet baking pans with a piece of parchment.
• Spread dollops of jam all over the dough.
• Scatter the whole blackberries over the dough.  You can chop them or crush them lightly if they seem too chunky to you.
• Roll up the dough over itself along the long edge into a tight log.
• Eyeball or use a measuring tape to mark the dough for cutting the rolls
  into 16 pieces.
• Run a length of dental floss under the dough. Cross the ends over each
  other with opposite hands and pull on the floss to cut a roll.
• Place the cut roll on the prepared pan.
• Continue cutting the rest of the rolls. Put no more than 8 rolls on a pan.
• Cover the rolls with a clean tea towel and let them rise at room
  temperature for 30 minutes to 1 hour.  Rolls are ready to bake when they’re visibly
  puffy and light.
• Towards the end of the rising time, preheat the oven to 350F (180 C).
• Bake the rolls for 20-25 minutes until golden brown and set. Set the pan on a wire rack to cool while you make the icing.

Make the icing:

• Beat all the ingredients together into a smooth icing.
• Use a spoon to spread a dollop of the icing all over the top of each roll.

Rolls are best eaten the same day
that they’re made, but you can freeze them without the icing in an airtight bag
for up to 1 month. To reheat, warm them in a pan in a 300F degree oven for 15
minutes. From there you can ice them.