Bring broth to a rapid boil, add the meatballs, and cook until heated through, about 10 minutes. Drain meatballs and reserve broth.

In a large skillet, melt the butter and cook the shallots until soft. Stir in the flour and cook until the sauce bubbles. Slowly stir in about 1-1/2 cups of the chicken broth. Simmer and stir occasionally until smooth and thick.

In a small bowl, beat the egg yolk until pale-colored. Slowly whisk in a few tablespoons of the reserved broth. This will warm the yolk and prevent it from curdling when added to the sauce Reduce the heat to low and whisk the yolk and broth mix into the sauce. Cook, Stirring constantly, until the broth is slightly thickened. Do not boil.

Add capers, lemon juice and pepper to the sauce and add more broth if needed. Add meatballs. Serve hot over noodles.