Combine the bulgur with 1 1/2 cups of water in a small saucepan. Bring to a boil, reduce heat to medium low, cover and simmer until tender, 10 to 12 minutes. Drain off the excess water and cool the bulgur completely.
Heat the oil in a small skillet over medium-high heat. Add the tomato paste, chili powder, cumin and cayenne and whisk until the oil is yellow and the spices are fragrant, about 45 seconds. Remove from the heat and let the chili oil cool to room temperature.
Whisk together the sour cream, lime zest and juice, a pinch of salt and 1 tablespoon water in a small bowl. Refrigerate until ready to serve.
Position an oven rack at the top of the oven and preheat the broiler. Line a baking sheet with foil. Combine the beans, cooked bulgur, cheese, breadcrumbs, 1 scallion, chili oil and 1/2 teaspoon salt in a large bowl. Use a potato masher to mash and combine the mixture until it holds together when squeezed. Form into 8 uniform cakes about 3/4-inch thick.
Arrange the cakes on the prepared baking sheet and generously coat each with cooking spray. Broil until a golden-brown crust forms, 3 to 4 minutes. Remove the baking sheet from the broiler and use a metal spatula to flip each cake. Coat the tops of the cakes with cooking spray and continue to broil until the tops are golden brown, 3 to 4 minutes.
Spread the romaine on a platter, transfer the chili cakes to the platter, drizzle with the sour cream mixture and sprinkle with cheese and the remaining scallion.
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