Start by making the dough: in a small bowl mix together flax and 3 tbsp warm water. In a large bowl, dissolve 1 tsp sugar into 1 cup water and sprinkle on yeast. Let both bowls sit for about 10 minutes until flax mixture is thickened and yeast mixture is foamy.
To the yeast mixture, add flax egg, vanilla, lemon juice and oil. In a separate bowl, mix together remaining sugar, 3 cups flour and salt. Add to the wet ingredients and stir until a shaggy dough comes together. Begin kneading, adding the remaining 1/2 cup flour as needed until you have a soft, uniform ball of dough. Place is a greased bowl and turn to coat. Cover and let rise until doubled, about an hour.
After risen, roll out dough on a floured surface to a thin triangle, about 13" by 18". Brush with the 3 tbsp of melted coconut oil.
To make the filling, combine coconut sugar with cinnamon and a pinch of salt. Sprinkle evenly over the oiled dough. Next, evenly sprinkle on the diced apple.
Tightly roll up the dough starting with a long edge. Place seam side dough and cut the dough log into even pieces, about 12.
Generously grease a large skillet or rectangular pan and arrange the cut rolls with even spaces between them. Brush with soy milk or additional melted coconut oil, if desired. Set aside to rise a second time, for about 30 minutes. The rolls should be fitting together snugly after the second rise.
Bake is a 350F oven for 30 to 34 minutes, until the tops are golden.
To make the caramel (note, you can start the caramel during the second rise of your buns)
Place the apple juice in a saucepan over high heat and bring to a gentle boil. Immediately reduce the heat to a simmer and keep it simmering until the juice has reduced to about 1/4 of its original volume. It should be visibly thick (this took about 40 minutes for me, but keep checking. There's no need to stir or fuss over it while it's reducing, but mind it doesn't burn). Turn off the heat and add in butter or oil and stir in well. Drizzle caramel over warm buns and enjoy.