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1
Rinse spinach; drain briefly, then place in large glass bowl.
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2
Microwave spinach, uncovered, on high just until wilted, 1 to 1 1/2 minutes.
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3
Drain, then squeeze out as much liquid as possible.
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4
Combine garlic, lemon peel, and crushed red pepper in processor; blend until garlic is finely chopped.
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5
Add spinach, 2 cups (packed) arugula, pine nuts, and lemon juice; process until coarse puree forms.
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6
With machine running, gradually add oil in thin stream and blend until almost smooth.
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7
Mix in cheese.
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8
Transfer pesto to small bowl; season with salt.
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9
Do ahead: Can be made 6 hours ahead.
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10
Cover; chill.
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11
Combine ground beef, 1 teaspoon salt, 1/2 teaspoon black pepper, and 6 tablespoons spinach-arugula pesto in large bowl; mix lightly with fingertips or fork just until incorporated.
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12
Form meat mixture into six 3/4-inch-thick patties.
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13
Place patties on platter.
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14
Do ahead: Beef patties can be made 6 hours ahead.
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15
Cover and refrigerate.
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16
Prepare barbecue (medium-high heat).
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17
Grill burgers to desired doneness, about 4 minutes per side for medium-rare.
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18
Grill buns, cut side down, just until lightly toasted, about 1 minute.
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19
Build burgers with pesto, patties, mozzarella cheese, tomatoes, and arugula.
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20
Cover with bun tops.