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1
Preheat the broiler with a rack set about 4 inches from the heat source.
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2
Put 1/4 cup of the sour cream, 1/4 cup iced water mixed with ice cubes, the sliced cucumbers, garlic, scallion whites and a large pinch salt in a blender.
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3
Blend until mostly smooth, then add the tomatoes.
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4
Blend until smooth, then remove the small cap on the lid of the blender and slowly drizzle in 1/4 cup of the oil while the blender is running.
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5
Season with additional salt if needed.
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6
Place the soup in the freezer while you prepare the quesadillas.
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7
Place the cannellini beans and a pinch black pepper in a bowl, and roughly mash with the back of a fork.
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8
Place 2 of the tortillas on a baking sheet without letting them overlap.
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9
Brush one side of the tortillas with some of the remaining olive oil.
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10
Flip, so the oiled side is directly on the baking sheet.
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11
Divide the mashed cannellini beans between the two tortillas and use a fork or your fingers to spread the mixture evenly on the tortillas, leaving a 1/2-inch border around the edge.
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12
Lay 3 pieces of the cheese on top of the beans on each tortilla (it is okay if the cheese overlaps slightly).
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13
Top with the remaining 2 tortillas and brush the tops of the tortillas with the remaining oil.
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14
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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15
Use a spatula to flip the quesadillas and cook until the cheese is completely melted and the tortillas are crisp and lightly golden brown, about 1 additional minute.
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16
Cut each into 6 wedges.
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17
To serve, ladle (or pour directly from the blender carafe) the soup in to 4 chilled bowls and drizzle with additional olive oil and several grindings of freshly ground black pepper and some of the sliced green scallions.
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18
Serve 3 pieces of quesadilla on the side of each bowl of soup along with a dollop of the remaining sour cream and some pickled jalapenos.
