In a medium saucepan, bring 2 cups milk, the whole garlic cloves, bay leaves and 1/4 tsp. salt to a boil over medium heat. Boil until the liquid is reduced to 1 cup, about 40 minutes. Discard the bay leaves. Pour into a sieve set over a bowl and use a wooden spoon or spatula to press the soft garlic through. Whisk the sauce until smooth, then whisk in 1/4 cup EVOO; season with salt.
Meanwhile, separate the broccoli into 2- to 3-inch florets on their stems; trim the stems to about 4 inches long. Peel the tough skin from the stems, then halve each lengthwise.
In a large skillet over medium heat, cook the sliced garlic in the remaining 1 tbsp. EVOO, stirring, until lightly browned, 5 minutes. Add the broccoli; sprinkle with the crushed red pepper and 1/4 tsp. salt. Pour in 1/2 cup water; cover and cook, tossing occasionally, for 10 minutes, adding 1/4 cup water at a time as needed if the broccoli sears (it should be tender but still bright, and the pan should be dry). Uncover and remove the pan from the heat.
To serve, reheat the garlic sauce. Thin with more milk if desired. Serve the broccoli in a pool of the sauce.