Rinse the chicken under cool water and pat dry with paper towels. Season with salt and pepper. Place the chicken in a large stockpot over medium-high heat. Add the onions, carrots, celery, jalapenos, garlic, bay leaves, thyme, and enough water to cover the hen. Season again with salt and plenty of pepper. Bring to a boil, then reduce the heat to medium-low and simmer, uncovered, until the meat begins to fall off the bones, about 2 hours. Skim off any foam that rises to the surface while cooking. Remove from the heat and cool for about 20 minutes.
Strain the stock through a fine-mesh strainer, reserving the stock, chicken, and 1/2 cup of the cooked vegetables. Put the stock in a smaller stockpot over medium heat and bring to a gentle boil.
Remove the meat from the chicken, discarding the skin and bones. Tear the meat into smaller pieces and add to the stockpot.
Combine the flour, baking powder, salt, and shortening in a medium-size mixing bowl. With your hands, work the shortening into the mixture until it resembles coarse crumbs. With a fork, mash the reserved cooked vegetables. Fold them and the milk, 1/4 cup at a time, into the flour mixture, being careful not to overwork the dough.
Lightly dust a work surface and your hands with flour. Turn the dough out onto the floured surface. Dust the top of the dough with flour. With your fingers, lightly press the dough out very thin, about 1/8 inch thick, dusting as you work. With a sharp knife, cut the dough into strips about 4 inches long and 1/2 inch wide. Set aside.
Add the heavy cream to the chicken stock and stir to mix. Gently drop the dumplings into the mixture and cook, stirring occasionally, until the dumplings are cooked through, about 30 minutes. Remove the bay leaves, stir in the green onions and parsley, and serve hot.
Yield: 6 to 8 servings