Melt butter in a small heavy-bottomed saucepan over medium-low heat. Whisk in flour and cook, stirring constantly, until bubbling but not browned, about 2 minutes.
Gradually whisk in stock, then cream. Bring to a simmer, cook for 30 seconds, then remove from heat and set aside to cool for 5 minutes. Sauce will thicken as it rests.
Stir in eggs and capers. Season to taste with salt and pepper. Keep warm over lowest heat until ready to serve.