Melt 3 tablespoons butter in a medium saucepan over medium heat and add the flour. Cook, whisking constantly, until the butter begins to toast the flour, about 3 minutes. Add the rosemary and nutmeg and whisk for 15 seconds to toast. Add the milk. Bring the sauce to a simmer and cook for 5 minutes over low heat, stirring occasionally. Add the blue cheese and whisk until melted. Set aside over low heat to keep warm.
Bring a pot of salted water to a boil. Set up a bowl of ice water and set aside. Line a tray with paper towels.
Trim the broccoli stems and break the heads into equal-size florets. Add the broccoli to the boiling water and let cook until bright green and tender but still with a slight resistance when pierced with a knife, 3 to 5 minutes. Transfer the broccoli to the ice bath for about 10 seconds just to shock and stop the cooking. Using a spider or a slotted spoon, transfer the broccoli from the ice bath to the paper towel-lined tray. Give the tray a good shake to get any excess water off the broccoli. Set aside.
Heat the remaining 2 tablespoons butter together with the olive oil in a large cast-iron pan over medium heat. Add the shallots and garlic and cook until softened, 3 to 4 minutes. Season with salt and pepper. Add the broccoli and toss gently with a wooden spoon or tongs to coat. Cook until heated through, 2 to 3 minutes.
Remove the broccoli from the heat and ladle the warmed blue cheese sauce over the top. Garnish with the minced Fresno and freshly ground black pepper.
The rosemary and nutmeg can also be steeped in the warmed milk instead of being added to the roux.