Prep ingredients. Preheat oven to 350 degrees F. Thaw phyllo according to package instructions (usually in the fridge overnight or for a few hours prior to cooking). In a small bowl melt 2 tbsp butter and mix in 2 tbsp olive oil, set by your workstation with a pastry brush.
Prepare phyllo. Set stack of phyllo sheets next to you and keep covered with a clean damp kitchen towel, working with one sheet at a time. Place one sheet of phyllo on a clean flat surface. Brush the phyllo with butter/oil mixture until coated. Layer another sheet of phyllo on top and brush with butter/oil.
Wrap the feta blocks. Place one 3 oz block of feta towards the bottom center of the phyllo, the short side closest to you. Wrap the feta by folding the bottom flap over first and then folding the two long sides over to almost cover the feta. Continue to brush the uncovered parts of the phyllo with butter/oil, as needed. Fold the feta block over, moving away from you. Repeat until feta is fully wrapped in the phyllo. Brush the top layer with more butter/oil. Repeat with second block of feta and 2 more sheets of phyllo.
Bake. Place wrapped feta blocks, seam side down, on a baking sheet. Bake at 350 F for 15 minutes. Remove from oven, carefully turn feta over to the other side, return to oven and cook for 10 more minutes. Both sides should be crispy and golden, if not continue cooking for 5 more minutes.
Add toppings & serve. Carefully transfer to a serving plate and immediately drizzle with warm honey. Sprinkle with an equal amount of white and black sesame seeds and top with fresh thyme.