In a mixing bowl combine ketchup, 1 tablespoon oil, brown sugar, lemon juice, chili powder, ground cumin, hot sauce, salt, and pepper; whisk until thoroughly combined.
Remove 2 tablespoons of the prepared barbecue sauce and set it aside.
Add shrimp to the bowl; lightly toss around to combine, and set aside for 10 to 15 minutes.
Heat ½ tablespoon oil in a large skillet over medium-high heat.
Add shrimp to the hot oil and cook for 2 to 3 minutes; flip over and, using a pastry brush, brush on reserved barbecue sauce, and continue to cook shrimp for 2 more minutes, or until cooked through. Cooked shrimp have a pink exterior with red tails and the flesh is slightly opaque and a little white in color.
Remove shrimp from skillet and transfer to a serving plate.
Garnish with lemon slices and parsley.