Preheat the oven to 350° F.
Rub the brisket with the salt and pepper and place it, fat-side-up, in a roasting pan. Pour in enough water to come about two-thirds up the sides of the brisket. Sprinkle the carrots and garlic into the water around the roast.
Roast the brisket, without covering it, until it is browned and tender, about 3 hours, spooning the pan drippings frequently over the meat. If necessary, add a little extra water during the cooking to keep the liquid at
least halfway up the sides of the brisket. Transfer the brisket to a serving platter.
To make the delicious gravy: Skim off any fat from the drippings into large skillet. You need 3 tablespoons of fat; if necessary, just add a little butter to equal this amount. Strain the drippings into a large heatproof measuring cup, reserving the vegetables for the gravy, if you wish.
Heat the fat in the skillet over medium-high heat. Add the garlic and cook until it begins to soften. Whisk in the flour and cook, stirring constantly, until the flour mixture bubbles all over, about 2 minutes. Gradually pour in the straining drippings and continue cooking and whisking until the gravy thickens. Remove the gravy from the heat and stir in the reserved vegetables, if you wish.
To serve: Slice the brisket on the diagonal, about 1/2-inch thick. Serve it up hot with a generous helping of gravy ladled over the top. This goes great with mashed potatoes.
Makes: 6