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1
Heat the oven to 375 degrees F and arrange a rack in the middle.
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2
Peel any loose outer skins from the garlic heads and cut off the top quarter of each head to expose the cloves.
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3
Place the garlic heads, cut side up, on a large piece of foil, drizzle 1 tablespoon of the oil over all 3 heads, and wrap tightly to form a foil packet.
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4
Place the packet on a baking sheet and bake until the garlic cloves are golden brown and very tender, about 60 to 75 minutes.
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5
Remove from the oven, open the packet, and let the garlic sit until cool enough to handle.
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6
Squeeze the roasted cloves from their skins and place in a small bowl; set aside.
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7
Heat the remaining 2 tablespoons oil in a large saucepan over medium heat until shimmering.
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8
Add the leeks, bay leaves, and rosemary, season with salt and pepper, and cook, stirring frequently, until the leeks have begun to soften and the herbs are fragrant, about 4 minutes.
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9
Add the potato, roasted garlic, and paprika, season with salt and pepper, and stir to combine.
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10
Cook, stirring occasionally, until a bit of crust begins to form on the bottom of the pan, about 10 minutes.
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11
Add the broth and, using a wooden spoon, loosen the crusty bits from the bottom of the pan.
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12
Reduce the heat to low, cover with a tightfitting lid, and let simmer until the potatoes are knife tender, about 15 minutes.
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13
Discard the bay leaves and remove the pan from the heat.
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14
Using a blender, puree the soup in batches until smooth, removing the small cap from the blender lid (the pour lid) and covering the space with a kitchen towel (this allows steam to escape and prevents the lid from popping off).
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15
Place the blended soup in a clean saucepan.
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16
(Alternatively, you can use an immersion blender to puree the soup in the original saucepan.)
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17
Return the soup to a simmer over low heat.
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18
Add the kale and water and stir to combine.
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19
Cover and cook, stirring occasionally, until the kale is tender but still brightly colored, about 10 to 12 minutes.
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20
Taste and add more paprika, salt, and pepper as needed.
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21
Ladle the soup into bowls, drizzle with olive oil, season with pepper, and top with a poached egg if desired.
