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1
Heat the oven to 325 degrees F and arrange a rack in the lower third.
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2
Using a paring knife and starting at the tapered end of the shank, cut between the meat and bone and work down the bone to create a pocket about 3 inches long.
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3
Stuff each lamb shank with 3 garlic cloves and season well with salt and freshly ground black pepper.
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4
Heat 1 tablespoon of the olive oil in a large Dutch oven or deep oven-safe pot with a tightfitting lid over medium-high heat.
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5
When the oil smokes, add the shanks and cook until well browned on all sides, about 7 to 10 minutes.
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6
(You may need to do this in 2 batches.)
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7
Remove to a plate and set aside.
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8
Remove the pot from heat until no longer smoking.
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9
Add remaining 1 tablespoon olive oil and return to the stove over medium heat.
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10
Once oil shimmers, add celery, carrot, and onion, season with salt, and cook until softened, about 4 minutes.
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11
Increase heat to medium high, add wine or water, and cook, scraping up any browned bits.
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12
Increase heat to high and nest shanks among vegetables, then add broth and any accumulated juices (the broth should surround, but not cover, the shanks).
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13
Bring to a simmer.
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14
Once simmering, cover and transfer to the oven.
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15
Braise the shanks, turning every 45 minutes or so, until the meat is fork tender, about 1 1/2 hours.
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16
Uncover and cook, turning once, until the meat is fork tender and falling off the bone, about 25 minutes more.
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17
Meanwhile, make the pesto.
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18
In the bowl of a food processor fitted with a blade attachment, combine mint, parsley, orange juice, salt, and garlic and process until smooth.
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19
With the processor running, add oil in a thin stream until evenly incorporated.
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20
Stir in orange zest and set aside.
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21
Remove the lamb from the oven, transfer to a plate, and strain the sauce through a fine mesh strainer into a bowl.
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22
Discard the vegetables and return the sauce to the pot.
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23
Add pesto, stirring to combine, then return the shanks to the sauce, turn to coat, and cook over low heat until warmed through.
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24
Taste the sauce and add salt and pepper as needed.
