Preheat a charcoal or gas grill to medium high. Skewer the strawberries and coat with 2 teaspoons vegetable oil. Grill until lightly charred on all sides, 1 1/2 minutes total.
Remove the strawberries from the skewers. In a medium saucepan, combine the strawberries, ketchup, jam, balsamic vinegar, molasses, soy sauce, mustard, chile and garlic. Cook over medium-low heat until the strawberries start breaking down, 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 sauce is reduced by one-third, about 15 minutes.
In a medium enameled cast-iron skillet or nonreactive Dutch oven, heat the remaining 2 teaspoons vegetable oil. Add the onion and bell pepper and saute until soft, about 4 minutes. Add the pinto beans and 1 1/2 cups of the barbecue sauce (reserving the rest for future use). Put the skillet in the oven and cook until the sauce thickens, about 25 minutes. Transfer to a serving bowl and garnish with the parsley.