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Not sure about EEA only, but Revolut might work for you and it has virtual cards.

Would be nice to have privacy.com more widely available.

At Revolut you can only have one disposable virtual card active at any moment and they cannot be used for subscriptions/recurring payments.

You can have up to 5 non-disposable virtual cards.

Looks great, but they don't offer the service in my country :(