1. Trim any fat or membrane from the giblets. The liver should not have the gallbladder (a small green sac) attached. If it is, trim it off carefully, removing bits of the liver if necessary. Do not pierce the sac; the liquid it contains is very bitter. Rinse giblets and neck, and pat dry.

2. In a medium saucepan, melt 3 tablespoons butter over medium heat. Add onion, celery, and leek. Cook, stirring occasionally, until onions are translucent, about 8 minutes. Add salt and pepper, and cook 1 minute more.

3. Add the water, bay leaf, gizzard, heart, and neck (do not add the liver). Bring to a boil over medium-high heat, and reduce to a full simmer. Cook until gizzard is tender when pierced with a paring knife, about 45 minutes. Transfer gizzard, heart, and neck to a plate, and set aside. The liquid should be released to about 3 cups; if not, raise the heat, and cook 10 to 15 minutes more.

4. Meanwhile, finely chop liver. Melt remaining tablespoon butter in a small skillet over medium-low heat. Add liver, and cook, stirring constantly, until it no longer releases any blood, 3 to 4 minutes. Transfer to a plate, and cover with plastic wrap. Refrigerate until ready to use.

5. Strain stock through a fine sieve into an airtight container, discarding bay leaf; let stand until grease rises to the top, and skim off with a large spoon. Finely chop gizzard and heart, and pull meat from neck; add to stock along with reserved liver. Refrigerate until ready to use.