Add sliced shallots and cook, stirring, until golden brown, about 3 minutes.
Add mushrooms and ½ teaspoon salt and cook, stirring, until tender and they begin to release their juices, 3 to 4 minutes.
Remove from heat and set aside.
Gradually whisk in ¾ cup milk to cooled flour in saucepan until smooth paste forms; then gradually whisk in remaining 1¼ cups milk until no lumps remain.