Grind clam meat in a meat grinder through large holes or food processor until roughly chopped and reserve.

Melt butter in a large stockpot over low heat. Cook onions until soft, about 5 minutes. Add clams and cook an additional 3 minutes, stirring occasionally to avoid browning.

Add clam juice, turn heat to high, and bring to a boil. Add cream, return to a boil, then reduce to a simmer. Add carrots, celery, and potato. Cook over medium-low heat, uncovered, until vegetables are tender, about 10 minutes.

Make beurre manie by mixing butter and flour together with your fingers to form a smooth paste. Press onto ends of a whisk and stir into soup until completely and evenly dispersed. Stir in remaining ingredients, taste and adjust seasonings, and serve immediately.