To prepare salad, place potatoes in a large saucepan; cover with water. Bring to a boil. Reduce heat, and simmer 25 minutes or until tender. Drain; cool. Cut potatoes into 1/4-inch slices. Combine potatoes, red onion, and next 6 ingredients (through 2 tablespoons vinegar); toss gently.
To prepare dressing, heat 2 tablespoons oil in a small skillet over medium-high heat. Add 3/4 cup yellow onion to pan; sauté 3 minutes or until tender. Add 3/4 cup beer and next 4 ingredients (through pepper); bring to a boil. Cook until reduced to 1/2 cup (about 6 minutes). Place mixture in a food processor. Add mustard to food processor; process until smooth. With processor on, slowly pour remaining 2 tablespoons olive oil through food chute, processing until smooth. Pour dressing over potato mixture; toss gently. Serve immediately.