Preheat the oven to 400°F. Place the garlic in tin foil, drizzle with olive oil, fold to enclose, and roast until very tender and fragrant, about 20 minutes.
Remove the roasted garlic cloves from the head and place in a blender or food processor, along with the lemon, parmesan and chile flakes. Purée until smooth. With the motor running, drizzle in the oil until emulsified. Season with salt and pepper.
Bring a large pot of salted water to a boil. Add the spaghetti and cook according to package instructions. Drain the pasta, return to the pot, and drizzle with olive oil.
Place 1 inch of water and a metal steamer in a large pot. Place the zucchini, asparagus and snap peas into the steamer. Bring to a simmer and steam, covered, until the vegetables are bright green and crisp-tender, about 5 minutes. Drain the vegetables and run under cold water to stop the cooking process.
Add the vegetables and sauce to the pasta in the pot and toss to coat.
Divide the pasta and vegetables between plates, top with half of a burrata ball, pine nuts and parsley.