Remove the outer skin from the garlic and place the head in a small baking dish. Drizzle with 1/2 tsp. oil. Add 1/4 inch water to the dish. Roast, uncovered, in a preheated 375-degree oven until tender but still firm, about 30 minutes. Let cool slightly, then peel the cloves. Thinly slice and set aside.
Bring 3 cups water to a boil. Place bread in a shallow heatproof dish large enough to hold it in a single layer. Pour in enough boiling water to nearly submerge it. Let stand until the bread is saturated, 3 to 5 minutes. Transfer the bread to a colander in batches and gently press out the liquid. The bread should be somewhat moist, but not dripping. Tear it into irregular pieces and transfer to a large bowl.
In a large skillet, heat 1 Tbsp. oil over medium heat until shimmering. Add leeks, 2 Tbsp. water and 1/4 tsp. salt. Partially cover and cook, stirring occasionally, until the leeks are tender but still bright green, 5 to 7 minutes.
Add the leeks to the bowl of bread along with the sliced garlic, 1-1/2 Tbsp. oil, cheese, thyme, pepper and the remaining 1/4 tsp. salt; gently combine with your hands or a spoon.
Spread the mixture into a shallow baking dish large enough to hold it in a 1-inch layer, such as a 9x13-inch pan. Drizzle with the remaining 1 tsp. oil.
Bake until crisp and golden in spots, about 30 minutes. Serve warm.