Heat the oil in 4 to 5 quart Dutch oven or soup pot over medium until shimmering. Add the onion, celery, carrots, and pancetta, and saute until the onion is translucent (about 10 minutes). Stir in the garlic.
Add the veggie broth, mustard, beans, herbs, and bay leaf. Increase heat and bring to a gentle boil, then reduce heat to medium-low and simmer for 15 minutes.
Remove bay leaf.
Add the tortellini to the pot, and cook for 5 minutes.
Reduce heat to warm. Add the half and half or non-dairy milk and stir well.