Preheat a small saucepan on low heat and melt 2 tablespoons of French butter. Once the butter bubbles, add the chopped garlic. Pan-fry until garlic turns golden brown and crispy, then remove immediately. Let the fried garlic rest on a paper towel-lined plate to absorb excess butter. Set aside.
In a medium saucepan, melt 2 tablespoons of butter over low heat. Gradually add the flour, stirring continuously to prevent clumps. Slowly add chicken stock, whisking until smooth and thickened. Remove from heat, season with salt, and set aside.
Bring salmon to room temperature for 30 minutes. Pat dry and season the skin with salt. Heat a medium cast-iron skillet over medium heat, add 2 tablespoons of butter. Place the salmon skin-side down in the pan. Cook until the skin is golden and crispy, basting the flesh with butter. Cook until the salmon is flaky and easily separates along the white lines, about 10-15 minutes. Transfer to a bowl, peel off the skin, and set aside.
Add the prepared roux, minced shallots, parsley, mayonnaise, dill, lemon juice, black pepper, and ½ teaspoon kosher salt to the bowl with the salmon. Gently stir until combined, keeping the salmon chunky. Chill in the refrigerator for 1 hour or overnight for best flavor.
Garnish the chilled dip with crispy garlic topping. Serve with cornichons, crackers, and bread. Enjoy!
