Brown bacon in a 3-quart saucepan with oil over medium heat. Remove cooked bacon. Add carrots, celery and onion and cook about 3 to 4 minutes to soften. Remove.
Place split peas and broth in the saucepan. Bring to a boil. Reduce heat and simmer, uncovered for about 30 minutes, stirring frequently.
Add vegetables, ham, bacon and thyme. Simmer an additional 30 to 40 minutes until peas are soft, not mushy. Add salt and pepper to taste.