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TOMATOES:
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Cut tomatoes in half lengthwise.
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Lay halves cut side up in a single layer in an 8- by 12-inch oval or rectangular casserole (rim should be at least 1/2 inches higher than tomatoes).
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In a 1 1/2- to 2-quart pan, combine onion, vinegar, sugar, olive oil, crushed red pepper flakes(if usng) and ginger.
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Bring to a boil over high heat, stirring often.
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Pour over tomatoes.
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Roast in a 400u00b0F oven (convection not recommended) until tomatoes are dark brown and sauce is browned and thickened (bubbles will be large and shiny), about 1 1/4 hours; baste tomatoes with sauce and onions about every 15 minutes at first, then more frequently as mixture begins to thicken, to avoid scorching.
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Use hot, warm, or at room temperature.
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ASSEMBLY:
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Spread lemon cheese equally on oiled sides of the olive-oil toast slices.
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Set on plates and cover equally with arugula leaves.
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Spoon tomatoes and juices equally onto toast slices.
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Add salt to taste.
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LEMON CHEESE:
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In a food processor or bowl, combine cream cheese (at room temperature), fresh chevre (goat cheese), milk, and grated lemon peel.
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Whirl or beat with a mixer on medium-high speed until blended.
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OLIVE OIL TOAST:
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Lay 8 slices of rustic white bread such as sourdough or ciabatta (about 3 by 4 in., cut about 1/2 inches thick) in a single layer in a shallow 10- by 15-inch pan.
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Bake in a 375u00b0F oven until lightly browned on the bottom, 5 to 6 minutes.
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Turn slices over and brush equally with about 2 tablespoons extra-virgin olive oil.
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Continue baking until golden brown and crisp, 6 to 8 minutes longer.
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Use warm, or let cool on a rack.