Pour great northern beans into a saucepan and cook over medium heat until very soft, about 30 minutes.

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At the same time, place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until fork-tender but not mushy, about 12 minutes. Drain.

Transfer beans to a large bowl. Add avocado and mash. Add mustard, yeast, lemon juice, and salt; stir until mixture is smooth. Add potatoes, celery, and onion and mix well.

Chill for at least 30 minutes before serving.