Cook oysters and reserved liquid in a skillet over medium heat until edges curl, about 5 to 10 minutes. Remove skillet from heat.

Combine onion, potato, broccoli, water, and corn in a saucepan; bring to a boil. Reduce heat and simmer until vegetables are tender, about 10 to 15 minutes. Drain vegetables and reserve liquid.

Melt butter in a large pan over medium heat. Stir flour into melted butter until smooth, about 1 minute. Slowly pour reserved vegetable water and milk into butter-flour mixture; cook until thickened, about 5 minutes.