Preheat the oven to 450 degrees F. (Make sure your oven is clean or it will smoke!)
Melt the butter in a small saucepan over low heat. Add the garlic, stir to coat with the butter, and cook, covered, for 20 minutes, stirring occasionally, until the garlic is very tender. Transfer to a small bowl and set aside until cool enough to handle. Mash the garlic in the butter with a fork. Stir in the Parmesan, parsley, lemon zest, red pepper flakes, 1 1/2 teaspoons kosher salt, and 1/2 teaspoon black pepper.
Slice the baguette in half lengthwise and place both halves, cut sides up, on a cutting board. Score each half diagonally (don’t cut all the way through) in large serving-size pieces. Spoon all of the garlic mixture generously on the cut sides of the bread. Cut each half of the baguette in half crosswise along a score and place the 4 pieces on a sheet pan lined with parchment paper.
Bake for 5 to 7 minutes, until the topping is bubbly and starting to brown and the bread is crisp. Transfer to a board, cut in serving pieces along the scores, sprinkle with fleur de sel, and serve warm.