Place asparagus into a large pot or skillet and cover with water; bring to a boil. Reduce heat to medium-low and simmer until tender, 8 to 10 minutes. Drain.
Mix 3 tablespoons butter and flour together in the same pot over medium-low heat until flour is dissolved and mixture is smooth, 2 to 3 minutes. Add milk, asparagus, and salt to butter-flour mixture and simmer until thickened, 10 to 15 minutes.
Spread about 1 teaspoon butter onto each piece of toast. Pour creamed asparagus over each piece of toast.