Step 1In a large pot, blanch the peas just until tender, being careful not to overcook. Immediately strain the peas and place in a large bowl of ice water to stop the cooking. Strain and reserve. Repeat with the pea tendrils.
Step 2In a large bowl using an immersion blender, or in stages using a regular blender, puree the peas and tendrils with the broth until smooth. Strain, then use the blender to blend in the d'espelette powder, olive oil and hot sauce.
Step 3The starch content of the peas may vary, affecting the thickness of the soup; if necessary, adjust the consistency of the soup with additional vegetable broth. Taste and adjust the seasoning as needed (vegetable broth varies in saltiness, more or less will be needed depending on your brand). If necessary, add sugar to taste for additional sweetness.
Step 4Serve the soup chilled.