Preheat a charcoal or gas grill to medium-high heat.
Skewer the strawberries and coat with 2 teaspoons of the vegetable oil. Grill on all sides, 1 1/2 minutes total.
In a medium saucepan, combine the strawberries, ketchup, jam, balsamic vinegar, molasses, soy sauce, mustard, chiles and garlic. Cook over medium-low heat until the strawberries start to break down and all the ingredients combine, about 15 minutes.
Preheat the oven to 300 degrees F.
Using an immersion blender, blend the strawberry mixture until smooth. Continue to cook until the mixture is reduced by a third, about 15 minutes. This will yield about 2 cups sauce.
In a medium cast-iron skillet, heat the remaining 2 teaspoons oil. Add the onions and bell peppers and saute until soft, about 4 minutes. Add the beans and 1 1/2 cups of the sauce. Put the skillet in the oven and cook until the sauce thickens, about 25 minutes. Garnish with parsley and serve.