Cook potatoes in microwave at HIGH 4 minutes; stir and cook in microwave 2 to 4 more minutes or until potatoes are tender. Let stand in microwave 10 minutes. Set potatoes aside.
Thaw Welsh rarebit in microwave at MEDIUM (50% power) 5 to 6 minutes.
Stir together potatoes, Welsh rarebit, milk, chopped green onions, and pepper in a medium saucepan over medium heat, and cook, stirring constantly, 10 minutes or until soup begins to simmer. Remove from heat; add cheese, and stir until cheese melts. Serve immediately.