Place the peeled and chopped potato pieces into a large pot and cover with cold water.
Add a generous pinch of salt.
Bring the pot to a boil over high heat and cook until the potato is tender when pierced with a knife, about 8 to 10 minutes.
Add the washed watercress to the boiling water with the potatoes.
Cook for just 1 minute, until the cress turns bright green and wilts.
Immediately drain the potato and watercress into a colander.
Using a rubber spatula or the back of a spoon, press firmly to squeeze out as much excess water as possible. This step is crucial for a thick purée!
Transfer the mixture to a food processor and pulse until it forms a coarse purée.
Add the extra virgin olive oil, sea salt, and white pepper. Process again until smooth and thoroughly combined.
Serve warm.