Heat oil in a large skillet over medium-high heat. Add garlic, oregano, paprika, salt and pepper; cook until fragrant, about 1 minute. Add steak strips; cook and stir until steak is browned and cooked through, about 5 minutes. Remove from heat.
Spread butter on one side of each slice of bread. Place two slices butter-side down on a work surface. Divide steak mixture between the two slices of bread; top with remaining two slices of bread so that the buttered sides are facing out.
Heat a large nonstick skillet over medium heat. Place sandwiches in skillet and cook until golden brown and cheese is melted, about 2 minutes per side.