There are countless versions of this simple, elegant stew. To achieve the perfect texture of just-cooked oysters, poach them in the milk until their edges begin to curl, set aside, and return them to the stew just before serving.
Drain oysters, reserving oyster liquor (about 1 cup). Heat milk and oyster liquor in a small saucepan over medium heat, whisking occasionally to prevent scorching, 3 to 4 minutes or until mixture just begins to steam. Add oysters, and season with desired amount of salt and pepper. Cook 4 to 5 minutes or until the edges of the oysters just begin to curl. Remove pan from heat. Using a slotted spoon, transfer oysters to a plate to prevent them from overcooking.
Melt butter in a large saucepan over medium heat. Add shallot and garlic, and cook, stirring often, 4 minutes or until tender. Sprinkle flour over shallot mixture, and cook, whisking constantly, 1 to 2 minutes or until completely incorporated and bubbly. Gradually whisk in half-and-half and next 3 ingredients. Bring to a boil, whisking constantly. Gradually stir in reserved milk mixture and oysters. Reduce heat to medium-low, and cook, stirring occasionally, just until warmed through. Season to taste with salt, pepper, lemon juice, and hot sauce. Serve with crackers.