Preheat oven to 425°F (220°C). Arrange broccoli florets on a baking sheet, drizzle with olive oil, and sprinkle with salt.
Roast broccoli for 20-25 minutes until tender. Smash each piece with a spoon to create flat, crispy bites. Return to oven for another 5-10 minutes until crisp.
Prepare soft-boiled eggs: Cook for 6 minutes for a runny yolk, then immediately transfer to ice water for 5 minutes. Peel gently.
Cook pappardelle according to package directions until al dente.
While pasta cooks, melt butter in a large skillet over medium heat. Add minced garlic and cook until fragrant (about 1 minute).
Whisk in hoisin sauce, honey, chili crisp, and white miso until mostly combined. Add reserved pasta water and bring to a gentle simmer.
Add cooked pappardelle to the skillet with the sauce. Toss gently for 3-5 minutes until the pasta is well-coated and the sauce has thickened slightly.
Serve immediately, topping each bowl with the smashed crispy broccoli, a soft-boiled egg, and an extra drizzle of chili crisp if desired.