Heat oil in an 8- to 10-quart pan over medium-high heat. Add sausages to pan and break into bite-size pieces. Stir occassionally until lightly browned, about 5 minutes.
Add onion, red pepper and garlic; saute over high heat until onion is soft, about 5 minutes. Stir in chili powder, cumin seed and oregano. Add broth, cover and bring to a boil over high heat. Add squash to soup. Return to a boil over high-heat.
Add squash to soup. Return to a boil. Reduce heat, cover and simmer until squash is tender when pierced, about 15 minutes, stirring occassionally.
Add hominy and peas, seperating if necessary. Bring soup to a boil over high heat and boil about 3 minutes.
Pour soup into a tureen and ladle into mugs or bowls. Add salt and pepper to taste.
If making soup ahead, don't add peas; cover soup when cool and chill, then add peas when reheating. For a tureen, use a rustic pan, such as a cast-iron Dutch oven. Or you can use a pumpkin shell. You'll need a pumpkin at least 12 to 16 inches tall and wide. Cut off top and scoop out seeds. About 10 minutes before serving, fill shell with boiling water to warm. Drain and fill with hot soup. Use the top as a lid for the pumpkin tureen.