Heat olive oil in a large pot over medium heat. Add onion and cook until softened, about 5 minutes.

Add peas and vegetable broth to the pot. Bring to a boil, then reduce heat and simmer for 15-20 minutes, or until peas are tender.

Carefully transfer the soup to a blender and puree until smooth and creamy. Return to the pot and simmer for 5-10 minutes to thicken.

Season with salt, pepper, cayenne pepper, and lime juice.

While the soup simmers, prepare the poached eggs. Fill a large skillet with water, add salt, and bring to a simmer. Crack eggs into the simmering water and cook for 3-4 minutes, or until whites are set and yolks are runny.

Stir heavy cream into the soup. Serve immediately, topped with a poached egg, fresh herbs, and a drizzle of olive oil.