1. Preheat the oven to 400°. Make the grits: In a small saucepan set over high heat, bring 1⅓ cup of the chicken broth to a boil. Stir in the grits, reduce the heat to low and cook until thick, about 10 minutes. Season with ½ teaspoon of salt and set aside.

2. In a large skillet set over medium heat, cook the bacon, stirring frequently, until crisp, 5 to 7 minutes. Transfer the bacon to a paper-towel-lined plate and set aside. Pour the bacon fat into a liquid measuring cup and add enough olive oil to measure ¼ cup total.

3. In a medium saucepan set over medium heat, combine the bacon fat-olive oil mixture with the garlic and cook until the garlic is pale gold, about 4 minutes. Stir in the celery root, chile and ginger and cook until softened, about 2 minutes. Stir in the leeks and season with salt. Cook until the leeks soften, 2 to 3 minutes, then add the thyme, rosemary, reserved bacon and tomatoes and cook, stirring occasionally, until ¾ of the liquid has evaporated, about 5 minutes.

4. Stir in the reserved grits and remaining 2 tablespoons of the chicken broth and continue to cook, stirring occasionally, until the mixture thickens slightly, 3 to 5 minutes. Turn off the heat and gently fold in the crabmeat and tarragon. Remove and discard the chile and herb sprigs.

5. Place four 8-ounce ramekins or oven-safe crocks on a rimmed baking sheet. Divide the crab and grits mixture evenly among the baking dishes, filling them ⅔ full. Use the back of a spoon to create a well in the center of each portion and carefully crack an egg into the well. Place the pan in the oven and cook until the egg whites are set, 30 to 40 minutes. Sprinkle with salt and pepper and serve.