Melt the butter in a small saucepan over medium heat.
Add the shallot and garlic. Sauté for 2–3 minutes, until the vegetables are soft and translucent.
Stir in the anchovy paste and cook for 1 minute, breaking it up with a spoon until it dissolves into the butter.
Deglaze the pan with the white wine or cider. Simmer for 2–3 minutes, until the liquid has reduced by half.
Add the cream and bring to a gentle simmer. Cook for another 3–4 minutes, stirring occasionally, until slightly thickened.
Whisk in the mustard (if using), season with black pepper, and add lemon juice for a touch of brightness.
Taste and adjust seasoning as needed. Serve warm.