How to Make It
Cut away the backs from the Cornish hens. Cut each hen into quarters. In a large pot, heat 1 tablespoon of the oil over moderately high heat. Add the backs and cook until very brown, about 8 minutes. Discard all but a teaspoon of fat. Add the onion, carrot and celery and cook 3 minutes longer. Add the wine and simmer 2 minutes, scraping the bottom of the pan to dislodge any brown bits. Add the stock. Bring to a boil and simmer until the stock has reduced to 2 cups. Strain the stock. Press the vegetables and bones firmly to get all the liquid. Set the stock aside.
Combine 1/2 cup of the flour, 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper. Dredge each hen quarter in the seasoned flour. In a frying pan, heat the remaining 2 tablespoons oil over moderately high heat. Add some of the Cornish hen quarters and cook until brown, about 4 minutes per side. Remove. Brown the remaining quarters.
In a large pot, heat the butter over moderate heat. Add the shallots and cook until beginning to turn golden, about 3 minutes. Add the remaining 1 tablespoon flour and cook, stirring, for 2 minutes. Add the hens with any juice that has accumulated, the reserved stock and the remaining 1 teaspoon salt. Bring to a simmer over moderate heat. Reduce the heat and cook, covered, at a bare simmer for 5 minutes. Add the asparagus and fresh peas, if using. Simmer until the hens are just done and the vegetables are tender, about 5 minutes longer.
Add the frozen peas, if using, the cream, lemon zest, tarragon and remaining 1/4 teaspoon pepper. Bring back to a simmer and serve.