In a Dutch oven, add oil and heat over medium-high heat. Add onions and saute until tender six to eight minutes. Add garlic and continue to saute until fragrant. Add the tomato paste and stir in, cooking for a minute or two until it just begins to lightly caramelize.
Working quickly so tomato paste doesn’t burn, add in the stock, then potatoes and carrots, and bring to a boil. Reduce heat, and simmer until the potatoes are nearly done, 15 minutes or so. At that point add the cabbage and simmer another 10 to 15 minutes or so until cabbage is tender. Add the corned beef to heat through, dicing first if necessary. Add the sugar, salt, and pepper to taste. A tablespoon or two of brine from leftover sauerkraut (if you have it on hand) or vinegar brightens this soup. If there is leftover sauerkraut available, omit the brine or vinegar and add in 1/4 to 1/2 cup.
Nutrition: Using smaller amounts of meat: Calories 180; Total Fat 3 g, 4 %; Saturated Fat 1 g 5 %; Monounsaturated Fat 0 g; Polyunsaturated Fat 0 g; Trans Fat 0 g; Cholesterol 12 mg 4 %; Sodium 265 mg 11 %; Potassium 1030 mg 29 %; Total Carbohydrate 33 g 11 %; Dietary Fiber 5 g 21 %; Sugars 9 g; Protein 8 g 16 %; Vitamin A 25 %; Vitamin C 113 %; Calcium 6 %; Iron 11 %