Heat a deep soup pot or Dutch oven over low heat. Dice the onion. Add olive oil to the pot, then add the onion, salt and pepper. Cook 5 minutes, stirring occasionally.
Coarsely chop the broccoli florets and add to the pot and stir. Trim woody ends off asparagus and chop in ½" pieces. Add to the pot and stir through. Pour in broth and increase heat to high until it comes to a boil. Reduce heat to medium and simmer 15 minutes.
Turn heat off and blend with an immersion blender until creamy and smooth.
In a separate bowl, whisk egg yolks and cream together. Add a ladle of the soup in and whisk well to temper the cream. Then pour the cream mixture into the soup, whisking constantly. Whisk in lemon juice.
Season to taste with salt, pepper and Tabasco hot sauce if using and serve while hot.
Notes
Vegetable stock can vary greatly in the amount of salt. Homemade stock is often much lower in sodium while store bought powders tend to be quite high in sodium. Taste your stock and if it is quite salty, wait until the end to add any salt if needed.