In a saucepan cook onion in 2 tablespoons of butter until tender. Stir in flour, tarragon, and black pepper. Add milk all at once; cook and stir until thickened and bubbly. Stir half of hot mixture into egg; return all to saucepan. Cook and stir for 1 minute more (don't boil!) Remove from heat, stir in spinach and feta then set aside.
Preheat oven to 375°F Brush a 12-inch pizza pan with some of the 1/3 cup melted butter; set aside. Unroll phyllo dough; remove 1 sheet of the phyllo dough at a time (As you work, cover remaining phyllo dough with plastic wrap to to prevent it from drying out) Lightly brush the first sheet with remainder of butter fold phyllo into thirds lengthwise to form a strip; brush the top butter. Place one end of strip in center of prepared pan, extending it over side of pan. Repeat with remaining phyllo dough and butter arranging strips spoke-fashion evenly around pan. (ends of strips will overlap in center and be about 3 inches apart at outer edges).