Melt the butter in a saucepan over medium heat and sprinkle in the flour. Make a roux by continually stirring the mixture until it's light brown.
Lower the heat to almost nothing. Add the mushrooms and green onions, and stir lightly to blend into the roux. The heat of the roux will cook the mushrooms and onions, and the vegetables will bring the heat of the roux down so it won't brown any further.
Add the Worcestershire, Tabasco, and chicken stock. Whisk to blend into a smooth sauce.
Add the peas and raise the heat a little. Cook until the peas are heated through, stirring while they're still frozen to blend them into the sauce. The sauce should have about the texture of gumbo. If it's too thick, add a little more stock or water.
Check the seasonings and add salt and pepper to taste.
