Melt the butter in a large pot over medium heat. Stir in the garlic, onion, and morels; cook, stirring frequently, until the onions have softened and turned translucent, about 5 minutes. Stir in chicken soup base and flour; cook for 1 to 2 minutes. Pour in water and cream; bring to a simmer, and cook 5 minutes.
Puree half of the soup in small batches, filling the blender no more than halfway full each time. Return soup puree to pot. Cook on low 10 to 15 minutes. Season with thyme and salt and pepper before serving.
