Prepare the carrot: peel and halve lengthwise. Cut each half again, lengthwise. Cut length into thirds; 12 sticks, total.
Brown the sausage in a large soup pot. Remove and slice into rounds; set aside.
Add the stock, garlic and several grindings of pepper to the soup pot. Bring to a boil, reduce heat and simmer, scraping all the browned bits from the bottom of the pan. Add the beans and cook, covered, for 60 to 90 minutes. Uncover and add the sausage and escarole and cook until escarole is soft. Taste and adjust seasonings. Serve with plenty of freshly grated Romano.
[MC-Per Serving: 727 cals, 47g total fat (61%cff)] VARIATION: Omit the sauce, cool overnight and slice thin. Serve for a buffet or take on a picnic.