How to Make It
Preheat the oven to 400°. In a large, deep skillet, heat 2 tablespoons of the olive oil. Add the pancetta and cook over moderate heat until crisp, about 6 minutes. Add the leeks and garlic, cover and cook, stirring occasionally, until the leeks are softened and starting to brown, about 10 minutes.
Add the wine to the skillet and cook over moderately high heat until reduced by one-third, about 5 minutes. Add the plums, cover and cook, stirring occasionally, until just softened, about 5 minutes. Transfer the contents of the skillet to a large bowl and let cool to room temperature. Stir in the bread crumbs, thyme and 1/4 cup of the parsley. Season with salt and pepper.
Fill the cavities of the hens with the plum stuffing. Twist the wings behind the backs and tie the legs together. Spread the celery root in a single layer on 2 large rimmed baking sheets. Drizzle with the remaining 1/4 cup of olive oil and season with salt and pepper. Arrange the hens on top of the celery root breast side up, drizzle with olive oil and season with salt and pepper. Turn the hens breast side down. Carefully pour the chicken stock into the baking sheets, cover with foil and roast in the oven for 45 minutes.
Turn the hens breast side up and roast, uncovered, for about 30 minutes longer, switching the baking sheets halfway through. The hens are done when they're golden brown and an instant-read thermometer inserted in the inner thighs registers 160°. Transfer the hens to a work surface and let rest for 10 minutes.
Meanwhile, using a slotted spoon, transfer the celery root to a platter and garnish with the remaining 1/4 cup of parsley. Transfer the pan juices to a bowl and skim off any fat; season with salt and pepper. Transfer the hens to plates and serve with the stuffing, celery root and pan juices.