In a small saucepan, use a whisk to combine the ketchup, rice wine vinegar, garlic, ginger, gochujang and soy sauce to make the BBQ sauce. Set the saucepan over medium heat until the sauce starts to simmer. Once simmering, reduce the heat to low and allow to gently simmer for 20 minutes, stirring occasionally to avoid burning the sauce. Remove from the heat, cover and refrigerate the sauce until ready to use, up to 2 days.
On the grill or in a sauté pan, cook the burgers 3 minutes on each side, until internal temperature is 165°. Brush melted butter on the cut sides of the buns and place the buns cut sides down on the grill or pan for up to a minute, or until the buns are golden brown.
To assemble the burgers, place a Beyond Burger on the bottom bun and then top each burger with the desired amount of BBQ sauce, half of the kimchi and the top bun. Enjoy immediately.