Heat oil in a skillet over medium heat; stir in green onions. Cook and stir until wilted, 3 to 5 minutes. Increase heat to medium-high. Pour in milk; cook until milk starts to bubble. Reduce heat and simmer until mixture thickens, 7 to 10 minutes. Add beans, salt, and pepper. Simmer until sauce thickens to a stew-like consistency, about 10 minutes.
Bring a large pot of lightly salted water to a boil. Cook egg noodles in the boiling water, stirring occasionally, until tender yet firm to the bite, about 6 minutes. Drain and return to pot. Stir in the sauce and serve.