Melt butter and oil in a medium saucepan on medium heat. Add ginger, leeks, and potato; cook, stirring occasionally until soft, 10 to 15 minutes. Stir in flour; cook for 1 minute.
Raise heat to medium-high and slowly pour in milk and reserved oyster liquor (1/4 cup), whisking constantly. As soon as bubbles begin to form around the edges of the pan, gently stir in oysters and cook just until set, about 2 minutes. Season to taste with salt and pepper. Divide among bowls.