Heat olive oil in a Dutch oven over medium heat.
Cook prosciutto until crispy, 5 to 7 minutes. Set aside. Crumble when cooled.
Cut tips from asparagus; add to pan. Cook, stirring occasionally, until crisp-tender, about 3
minutes. Set aside with prosciutto.
Roughly chop remaining asparagus; add to pan with leeks, salt, and pepper. Cook, stirring
occasionally, until slightly softened, about 5 minutes.
Add garlic; cook 1 minute more. Add peas, stock, and thyme.
Cover, and cook until asparagus is very tender, about 30 minutes.
Remove thyme sprig. Stir in parsley, lemon juice, and lemon zest.
Using an immersion blender (or transferring soup to a blender), blend soup to desired consistency.
Add ¼ cup cream; blend until combined. Taste, and add salt and additional cream, if desired.
Garnish servings with crumbled prosciutto and asparagus tips.