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1
Puree tomatoes with their puree in a blender.
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2
Heat oil in a large heavy pot over medium-high heat until it shimmers, then saute onion until golden, 5 to 6 minutes. Add garlic and saute 1 minute. Add tomato puree, sugar, and salt and simmer, uncovered, stirring occasionally, until thickened, 30 to 35 minutes.
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3
Stir together bread crumbs and milk in a large bowl and let stand for 10 minutes.
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4
Stir in eggs, cheese, garlic, parsley, oregano, and salt, then add turkey and blend with your hands until just combined well (do not overmix).
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5
Form 1 1/2-tablespoon portions into meatballs and arrange on 2 well-oiled large, heavy, rimmed baking sheets.
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6
Stir together butter, oil, garlic, salt, cheese, parsley, and pepper in a bowl. Spread about 2 rounded teaspoons garlic butter onto both split sides of each bun. Arrange buns, buttered sides up, on a large baking sheet.
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7
Preheat broiler.
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8
Broil meatballs 3 to 4 inches from heat, turning over once, until golden and just cooked through (165u00b0F on instant-read thermometer), 5 to 8 minutes.
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9
Broil buns, buttered sides only, until golden, 30 seconds to 1 minute, watching closely (buns brown fast).
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10
Spoon some sauce on each bun, then top with 4 meatballs (depending on size of buns), and drizzle with more sauce.