In a food processor add the cream cheese, 2 ounces of the smoked salmon, sour cream, mayonnaise, lemon juice, fresh dill, and garlic. Process until combined, scrape down the sides, and pulse until smooth.
Add the dip to a medium bowl and fold in the remainder of the 2 ounces of smoked salmon, chives, dill, capers, salt, and pepper. Mix with a spoon until combined.
Place the dip in the refrigerator and let it sit for at least 30 minutes. Serve with crackers, sliced cucumbers, bagel chips, or any of your favorite crackers and veggies.
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Store in an airtight container in the refrigerator for up to 5 days. We do not recommend freezing this dip.