Drain juice from clams into a 6-quart saucepan or stockpot over medium heat. Add the onions, celery, potatoes and carrots. If needed, add water to cover the vegetables, and simmer over medium heat until tender.
Meanwhile, in a 2-quart saucepan, melt the butter over medium heat. Whisk in flour until smooth. Cook for 1-2 minutes, until bubbly. Gradually whisk in half-and-half, about 1 cup at a time, and keep whisking until thick and smooth.
Add half-and-half mixture to pot with vegetables. Stir in clams just before serving. When clams are heated through, stir in seasoning, then salt and pepper, to taste.
Notes
To make this soup more budget-friendly, we recommend checking big retailers, like Costco, Sam's Club, BJs, Smart & Final, Amazon or Walmart online for large cans of minced clams.