Slice the green tops off the leeks and trim off the root bottoms. Discard, or save the green tops for broth. Cut the leeks in half lengthwise, then slice into 1/2-inch pieces. Place the chopped leeks in a bowl of cold water and swish to remove any sand or dirt. Use a slotted spoon to lift the leeks out, leaving the grit behind.
Add the butter and garlic to a skillet and cook over medium heat for 1 to 2 minutes, just until the butter melts and the garlic is fragrant.
Add the leeks and season with salt and pepper. Continue cooking and stirring for 5 minutes.
Add the broth and bring to a boil. Cover, reduce the heat to low, and cook for 8 minutes.
Uncover and increase the heat to medium. Add the half and half and parmesan cheese, stirring until melted and hot, about 2 to 3 minutes.
Remove from heat and serve immediately, topped with salt and pepper, red pepper flakes, and a squeeze of lemon juice if desired.