Preheat oven to 500°.
Heat oil in medium nonstick skillet over medium-high heat. Add seeds; sauté 30 seconds or until seeds begin to pop. Add blackberries, turmeric, and salt. Reduce heat; sauté 2 minutes or until berries are soft. Remove from heat; set aside.
Combine crabmeat, goat cheese, and chopped fennel fronds; shape mixture into 8 (1 1/2-inch) balls. Unroll phyllo dough; remove parchment paper. Reroll phyllo. Cut about one-fourth of phyllo roll crosswise into very thin slices to yield 2 cups (it should look like shredded cabbage). Reserve remaining phyllo for another use; store in a zip-top plastic bag in refrigerator. Fluff phyllo with fingers to separate strands. Press each crab ball into phyllo; roll until coated. Gently place on a baking sheet coated with cooking spray. Spray each ball with cooking spray.
Bake at 500° for 3 minutes or until phyllo is golden brown. Serve with blackberry chutney; garnish with fennel fronds, if desired.