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Step 1
Bring the eye of round to room temperature and pat it dry. Mix the spices, salt and pepper and rub all over the meat.
Step 2
To a suitably sized skillet over medium-high heat add the olive oil and sear the eye of round on all sides until it is nicely browned. Set it aside and lower the heat to medium.
Step 3
Saute the onion and garlic for 3-4 minutes, Stir in the tomato paste, cook 1 more minute.
Step 4
Add the wine or beer to deglaze the skillet. Scrape off any brown bits from the bottom of skillet and and bring to simmer. Stir in the brown sugar and thyme. Transfer all to the slow cooker.
Step 5
Place the browned roast on top of the braising mixture. Arrange the vegetables around the meat and add the beef stock. Close the lid and cook on low for 8 hours or until the meat is fork tender/on high for 5 hours or until the meat is tender.
Step 6
Once you are satisfied with the tenderness of the roast, remove it from the slow cooker onto a platter. Arrange the vegetables around it. Keep warm while you make the gravy (see steps below).
Step 7
Preheat the oven to 325 F.
Step 8
Complete steps 1 thru 4, but transfer the braising mixture to a suitably sized Dutch oven.
Step 9
Place the browned roast (and any natural juices from while it was resting) amidst the braising mixture. Arrange the vegetables around. Add the beef broth.
Step 10
Place the lid of the Dutch oven and cook in the oven for about 3-5 hours or until the roast is fork tender. (Begin checking after about 3 hours.)
Step 11
When you are satisfied with the tenderness of the beef remove it from the Dutch oven onto a platter, arrange the veggies around it and keep warm while you make the gravy.
Step 12
Strain the remaining braising liquid. Set aside.
Step 13
In a sauce pan over medium heat melt the butter and whisk in the flour. Gradually add the braising liquid (about 2 cups or just less) while continuing to whisk to make sure that no lumps form.
Step 14
Once the gravy has your desired consistency, remove it from the heat and transfer it to a gravy boat for serving with the eye of round roast.