Add the water and ½ tsp salt to a medium size saucepan and bring to a boil. Add the green beans and cook the beans for 3 minutes. Turn off the heat and transfer the beans to a bowl using a slotted spoon reserving the cooking water in the pan, set aside.
Melt the butter in a dutch oven over medium heat. Add the onion and cook, stirring occasionally, until softened, about 5 minutes.
Add the potatoes, garlic, paprika, ½ tsp salt, and ½ tsp pepper. Stir to combine.
Stir in 4 cups of the reserved cooking water and bring to a boil. Reduce heat to medium-low and simmer until potatoes are tender, about 15 minutes.
Use an immersion blender to puree the soup (or puree in batches in a stand blender or food processor).
Stir the green beans into the pureed soup then stir in the heavy cream. Simmer over medium-low heat until heated through.
Season soup with salt & pepper to taste.
