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1
Preheat oven to 350 degrees.
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2
Combine unpeeled garlic heads and unpeeled shallots in large bowl, pour the olive oil over them and toss to coat.
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3
Season generously with salt and pepper and place them in a single layer in a baking dish along with any oil remaining in bowl.
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4
Cover with foil and bake 35 minutes.
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5
If shallots are soft by then, remove them.
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6
Bake them a little longer if necessary.
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7
Continue baking the garlic another 30 minutes or so until it is soft.
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8
Allow garlic and shallots to cool.
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9
Meanwhile, melt the butter in a heavy three- to four-quart saucepan.
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10
Add onions and cook gently for 15 minutes.
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11
Do not allow to brown.
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12
Add peeled, unroasted shallots and peeled garlic cloves.
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13
Cook over low heat 10 minutes longer.
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14
Add potatoes, about 1/2 teaspoon salt or to taste, the chicken stock, cream and thyme.
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15
Cover and cook about 40 minutes, until potatoes are very soft.
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16
Peel roasted shallots.
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17
Cut roasted garlic heads in half horizontally and squeeze in a potato ricer or by hand to extract the soft pulp.
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18
Add garlic pulp and shallots to saucepan and cook 10 minutes longer.
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19
Puree the soup in a blender or food processor.
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20
Season to taste with salt and pepper and, if desired, adjust the consistency of the soup with some additional stock, cream or milk or water.
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21
Reheat before serving.