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1
Make the ketchup: heat oil in a small saucepan over medium heat; add in garlic and pepper flakes; cook for 1 minute.
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2
Add in ketchup and oregano; cook 2 minutes.
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3
Remove from heat and stir in vinegar and basil; season to taste with salt and pepper.
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4
Transfer to a bowl and let cool to room temperature or cover and refrigerate for 1 day; bring to room temperature before serving.
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5
Make the fricos: combine the cheese and flour in a bowl.
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6
Heat an 8 inch nonstick skillet over med-high heat; add 3 tablespoons of cheese mixture and cook until light brown on the bottom; turn over with a heat-proof silicone spatula and continue cooking for another 10-15 seconds.
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7
Remove to a plate to cool; wipe out the pan with a paper towel and repeat to make 3 more fricos.
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8
Divide the meat into 4 equal portions; 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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9
Season both sides of each burger with salt and pepper.
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10
Heat oil in a pan or griddle over high heat until the oil begins to shiimmer.
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11
Cook the burgers until golden brown and slightly charred on the first side, about 3 minutes for beef and 5 minutes for turkey.
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12
Flip burgers; cook beef burgers until golden brown and slightly charred on second side, 4 minutes for med-rare, 5 minutes for turkey.
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13
Place the burgers on the bun bottoms; add some of the arugula to each burger; top with the fricos, and then add a dollop of the ketchup.
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14
Top with the bun tops and serve immediately.
