Heat a medium saucepan over medium heat, then add the butter. When the butter is melted, add the flour and whisk until smooth.
Remove from heat and whisk in the heavy cream, 3/4 cup Parmesan cheese, and ground black pepper.
Adjust seasoning to taste then add the celery and gently stir to coat thoroughly. Transfer to a greased 1-quart baking dish.
Cover and bake for 20 minutes. While the celery is baking, use a microwave to melt the remaining 1 tablespoon of butter in a small bowl. Add the breadcrumbs, remaining 1 tablespoon Parmesan, and parsley; stir to combine.
Remove cover and sprinkle with breadcrumb mixture. Return to the oven and continue baking, uncovered for 10 minutes, until golden and bubbly. Serve hot.