Adjust oven rack to middle position and heat oven to 300 degrees. Thoroughly pat roast dry with paper towels; sprinkle generously with salt and pepper.
Heat oil in large heavy bottomed Dutch oven over medium-high heat until shimmering but not smoking. Brown roast thoroughly on all sides reducing heat if fat begins to smoke 8 to 10 minutes. Transfer roast to large plate; set aside.
Reduce heat to medium; add onion carrot and celery to pot and cook stirring occasionally until beginning to brown 6 to 8 minutes.
Add garlic and sugar; cook until fragrant about 30 seconds.
Add chicken and beef broths and thyme scraping bottom of pan with wooden spoon to loosen browned bits.
Return roast and any accumulated juices to pot; add enough water to cover halfway up sides of roast. Bring liquid to simmer over medium heat then place large piece of foil over pot and cover tightly with lid; transfer pot to oven. Cook turning roast every 30 minutes until fully tender and meat fork or sharp knife easily slips in and out of meat 3½ to 4 hours.
Transfer roast to carving board tent with foil to keep warm.
Allow liquid in pot to settle about 5 minutes then wide spoon to skim off excess fat from surface; discard thyme sprig. Boil over high heat until reduced to about 1½ cups about 8 minutes. Stir in flour stirring constantly until gravy obtains desired thickness. Season to taste with salt and pepper.
Slice roast; serve with gravy.
This recipe has been added to the following public cookbooks:
OnlineCookbook,
Bill Smith's Bests
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