Slice Kielbasa in half lengthwise then sliced diagonally into 3/4-inch pieces. Heat oil until hot, in a large skillet over medium heat. Add kielbasa and cook 5 minutes, or until browned.
Add garlic and onion; cook, stirring occasionally, 2 to 3 minutes or until translucent. Add 1/2 cup water to skillet and stir to deglaze pan; add cabbage and potatoes. Cook 10 minutes or until cabbage is wilted, stirring occasionally.
Turn heat to medium low. Add beer; cook covered 15 minutes until potatoes are tender. Remove cover; add salt and pepper. Stir to combine. Raise heat to medium and cook 15 more minutes until beer has reduced and is slightly saucy.