In medium bowl or stand mixer, dissolve yeast in warm water with sugar. Allow to sit 5 minutes, or until bubbly. Mix in flour, salt, and olive oil to form smooth dough. Add flour as needed until dough consistency is slightly tacky to the touch but not overly sticky. Let rise in greased bowl for 30 minutes.
Meanwhile, preheat oven to 350. Mix cream cheese, chicken, broccoli, garlic powder, salt, pepper, and ½ cup cheese.
When dough has risen, gently punch down, then roll out on a piece of parchment paper/silpat forming a rough rectangle approximately 15 by 20 inches (no need to be perfect!).
Spread chicken and broccoli mixture down middle of dough, then sprinkle with the remaining cheese. Using pizza cutter or sharp knife, cut one inch strips at a diagonal from outside of the rectangle to filling in the center. Fold the strips of dough over filling, alternating sides to make braid pattern. When you get to end of braid, tuck in ends.
Move parchment or silpat to baking sheet. Beat egg lightly with water and brush egg mixture over braid. Sprinkle lightly with sea salt.
Bake 25-30 minutes, or until light golden brown.