Generously coat a nonstick skillet with cooking spray and heat over medium heat.
Spread one side of each bread slice with softened butter. Sprinkle Parmesan over the buttered bread and gently press down.
On the two unbuttered sides, evenly place slices of Brie so that it mostly covers the bread. Sprinkle with basil and tarragon. On each slice, layer with alternating slices of apricot and avocado. Top with havarti. Place the other two slices of bread on top, buttered side facing up.
Place in skillet and cook until golden brown. Carefully flip and continue cooking until the other side is also golden brown and the cheese melts. Cut into halves and serve immediately. Enjoy!