Peel the cucumber. Cut it in half lengthwise and use a spoon to remove the seeds. Finely chop the flesh.
Place the chopped cucumber in a colander and sprinkle it with the coarse salt. Toss gently and leave it to drain over the sink or a bowl for 30 minutes.
Rinse the cucumber thoroughly under cold water to remove the excess salt. Transfer it to a clean kitchen towel and gently squeeze out as much moisture as possible.
Melt the butter in a saucepan over medium heat. Add the onion and cook for 3 to 4 minutes, stirring occasionally, until softened but not browned.
Add the drained cucumber and chopped spinach. Cook for another 4 to 5 minutes, stirring regularly, until the spinach has wilted and the cucumber has begun to soften.
Add the bay leaf and broth. Bring the soup to a gentle boil, then reduce the heat to low. Cover partially and simmer for approximately 25 to 30 minutes, or until the vegetables are very tender.
Remove and discard the bay leaf.
Blend the soup until completely smooth using an immersion blender. If using a countertop blender, allow the soup to cool slightly and blend it carefully in batches.
Return the soup to low heat and stir in the cream. Warm it gently for 2 to 3 minutes without allowing it to boil.
Taste before adding any additional salt, as the cucumber and broth may already provide enough. Season with freshly ground black pepper and serve warm.
