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1
To make the ketchup, heat the oil in a small nonreactive saucepan over medium heat.
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2
Add the garlic and chile flakes and cook for 1 minute.
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3
Add the ketchup and oregano and cook for 2 minutes.
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4
Remove from the heat and stir in the vinegar and basil and season with salt and pepper.
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5
Transfer to a bowl and let cool to room temperature or cover and refrigerate for up to 1 day.
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6
Bring to room temperature before serving.
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7
To make the fricos, combine the cheese and flour in a bowl.
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8
Heat an 8-inch nonstick pan over medium-high heat.
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9
Add 3 tablespoons of the cheese mixture and cook until light brown on the bottom.
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10
Turn over with a heat-proof silicone spatula and continue cooking for another 10 to 15 seconds.
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11
Remove to a plate to cool.
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12
Wipe out the pan with a paper towel and repeat to make 3 more fricos.
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13
Divide the meat into 4 equal portions (about 6 ounces each).
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14
Form each portion loosely into a 3/4-inch-thick burger and make a deep depression in the center with your thumb.
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15
Season both sides of each burger with salt and pepper.
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16
Cook the burgers, using the oil (see page 16).
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17
Place the burgers on the bun bottoms.
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18
Add some of the arugula to each burger, top with the fricos, and then add a dollop of the ketchup.
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19
Top with the bun tops and serve immediately.