Combine zucchini, onion, oregano and thyme in a large baking dish or sheet pan then toss with 2½ tablespoons olive oil, ½ teaspoon salt & fresh cracked black pepper. Nestle each half of the garlic head into the vegetables, cut side down.
Create a hole in the center and place feta block, drizzle with remaining olive oil. Roast until zucchini is tender and feta is caramelized, about 30-35 minutes.
Remove herbs and squeeze out roasted garlic. Transfer vegetables and cheese to the blender; add broth (use less for a thicker soup) and blend until smooth. Warm on the stove when ready to serve if you want it hot or eat chilled. Ladle soup into bowls; garnish with extra feta and fresh dill, plus a drizzle of olive oil, if desired.
Notes
This soup is not too thick. You can use less broth to make it thicker.