In a small saucepan, combine soy sauce, mirin, sake, honey, ginger, garlic, sesame oil, ketchup, and smoked paprika. Heat over medium-low, stirring until well combined. If you want a thicker sauce, dissolve ½ tsp cornstarch in 1 tbsp water and whisk it in. Simmer for 2–3 minutes until slightly thickened. Remove from heat and set aside.