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1
Heat a large saute pan or Dutch oven over high heat for 2 minutes.
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2
Swirl in 3 tablespoons olive oil, and add the onions, 1 teaspoon thyme, 1 teaspoon salt, and some pepper.
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3
Cook 6 minutes, stirring often, and then turn the heat down to medium.
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4
Add the butter, and cook 15 minutes, stirring and scraping with a wooden spoon, until the onions start to caramelize.
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5
Turn the heat down to low, and continue cooking for about 10 minutes, stirring often, until the onions are a deep golden brown.
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6
Remove the pan from the heat and set aside.
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7
Preheat the oven to 350F.
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8
Use a mandoline to slice the potatoes into 1/8-inch-thick rounds.
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9
Toss them with the cream, 1 teaspoon thyme, 1 teaspoon salt, and some freshly ground black pepper.
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10
Cut the tomatoes into 1/4-inch-thick slices, arrange them on a plate, and season them with 1 teaspoon salt and some pepper.
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11
Place half the caramelized onions in an even layer in a 9-by-9-inch (or equivalent) gratin or baking dish.
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12
Arrange one layer of alternating potatoes and tomatoes on top of the onion layer.
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13
Drizzle with 2 tablespoons of the cream from the potatoes and 1 tablespoon olive oil.
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14
Season with 1/4 teaspoon salt, a healthy pinch of pepper, 1/2 teaspoon thyme, and half the basil.
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15
Scatter the rest of the caramelized onions over the potatoes and tomatoes.
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16
Arrange another layer of potatoes and tomatoes on top; make this layer pretty, because it will be the top of your gratin.
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17
Pour the remaining cream (from the potatoes) and remaining tablespoon olive oil over the potatoes and tomatoes.
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18
Season with 1/4 teaspoon salt, a pinch of pepper, the remaining 1/2 teaspoon thyme, and the remaining basil.
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19
Press the vegetables down with your fingers.
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20
The cream and oil will come up through the layers and coat the vegetables evenly.
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21
Cover the baking dish tightly with aluminum foil.
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22
Bake about 2 hours, until the potatoes are tender when pierced.
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23
Remove the gratin from the oven and uncover it, being careful of the steam.
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24
Turn the oven up to 450F and return the gratin, uncovered, to the oven.
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25
Cook another 25 to 30 minutes, until the juices have thickened and the top is nice and golden brown (as in gratineed).
