Combine water and garlic in a large pot; bring to a boil. Add cauliflower and radishes; cook and stir until cauliflower is tender and easily pierced with a fork, 5 to 10 minutes. Strain, reserving cooking liquid; place the cauliflower mixture in a bowl.
Blend the cauliflower mixture with a handheld mixer, thinning with some cooking liquid, until smooth. Season with pepper and salt.