MICROWAVE METHOD: In microwave oven, melt butter in a 1-quart glass measuring pitcher for about 1 minute at HIGH.
Add grated onion and flour and mix well. Gradually add warm or room temperature chicken broth (NOT hot) and half-and-half to container, stirring constantly.
Cook uncovered for 5-6 minutes at HIGH or until sauce is thickened. Do NOT boil.
After 2 minutes, stir mixture, then stir again every 30 seconds to one minute as needed. When sauce reaches medium thickness, remove from microwave, add seasonings and stir. Mmmm!
STOVETOP METHOD: In a small saucepan, melt butter and stir in the flour, salt and white pepper. Add cold half-and-half and COLD chicken broth all at once. Stir well. Cook, stirring frequently, at medium heat until thick. Remove from heat and stir in seasoning.