Heat oven to 375°. Cut tomatoes in half crosswise. Use a spoon to gently hollow out inside of tomatoes, being careful not to puncture outer shell.
Melt butter in a skillet over medium-high heat. Add onions and celery and sauté until beginning to brown. Add water and scrape bits from bottom of pan.
In a large bowl, tear bread into bite-size pieces. Add seasoned breadcrumbs, onion mixture, and celery seed to bowl and season with salt and pepper.
Place tomato halves in a buttered casserole dish and fill each with breadcrumb mixture. Top each with cheese and drizzle with oil. (Optional: My mom would add a pinch of paprika and I instead add a sprinkle of chopped jalapeño. Also great without.)
Bake until tops are browned, about 20 minutes.