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1
Position a rack about 4 inches from the broiler heat source, and preheat.
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2
Blend 1/2 cup ice water mixed with ice cubes, 1/4 cup of the sour cream, cucumber, tomato, garlic, scallion whites and 1/2 teaspoon salt in a blender until completely smooth.
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3
Remove the small cap on the lid, and slowly drizzle in 1/4 cup of the oil while the blender is running.
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4
Season with additional salt if needed.
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5
Place the soup in the freezer while you prepare the quesadillas.
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6
Place the black beans and a pinch of pepper in a medium bowl, and roughly mash with the back of a fork.
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7
Place 2 of the tortillas on a baking sheet with no overlap.
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8
Brush the tops with some of the remaining olive oil, then flip so the oiled side is directly on the baking sheet.
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9
Divide the mashed beans between the 2 tortillas, and spread the mixture evenly with a fork or your fingers, leaving a 1/2-inch border around the edge.
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10
Sprinkle the cheese evenly on top of the beans.
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11
Top with the remaining 2 tortillas, and brush the tops with the remaining oil.
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12
Place the quesadillas under the broiler, and cook until the top tortillas are crisp and lightly golden brown, about 1 minute.
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13
Flip the quesadillas with a spatula, and cook until the cheese is completely melted and the tortillas are crisp and lightly golden brown, about 1 more minute.
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14
Cut each into 6 wedges.
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15
To serve, ladle (or pour directly from the blender carafe) the soup into 4 chilled bowls.
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16
Drizzle with olive oil, add several grinds of pepper and sprinkle with some of the sliced green scallions.
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17
Serve 3 quesadilla wedges on the side of each bowl of soup, along with a dollop of the remaining 1/4 cup sour cream.