In a large sauté pan over medium heat, melt the coconut oil. Add the anchovies and red pepper flakes and cook, stirring occasionally, until the anchovies dissolve into the oil, about 2 minutes.
Add the garlic and sauté for another minute.
Stir in the tomato paste and cook for 1 minute. Add the chopped tomatoes and cook another minute. Stir in the parsley, capers, and black pepper.
Add the celery pieces, stirring well to coat them in the sauce. Reduce heat to medium-low and braise for about 20 minutes, or until the celery is very tender.
Serve hot — and feel free to turn up the heat with an extra pinch of red pepper flakes!