Add all the coulis ingredients to a small sauce pan and simmer over medium heat for 2 minutes, stirring well. Remove from heat and let cool completely; refrigerate until chilled.
In a large bowl, place all the ingredients for the crab salad; mix well.
Drizzle avocado with lime juice, olive oil, and salt. Gently mash just enough to help hold the cubes together.
Assemble the stack
Place a lightly greased round mold on the center of the plate. Add the avocado layer first; gently press down (with a spoon) to make it as compact as possible.
Next, add a generous layer of the crab salad. Press down, and then gently remove the mold.
Spoon the tomato coulis around the stack. (You can also use a squeeze bottle)
If you saved some of the lump pieces of crab, add these on top.
You can also garnish the stacks with some additional parsley.