Methods

1. To make the spice rub for the duck, combine 1 tablespoon coriander seeds, 1½ teaspoons fennel seeds, and black peppercorns in a spice grinder and grind into a medium-fine powder. Add 1 tablespoon Byadgi chilli powder, turmeric, and 1½ teaspoons fine sea salt, and pulse to mix well, 5 to 10 pulses. 
2. Pat 4 bone-in, skin-on duck legs dry, place on a sheet pan, and sprinkle with the spice mixture, making sure all sides are liberally seasoned. Cover and refrigerate for at least 8 hours, but preferably 24, up to 48 hours.
3. Preheat the oven to 325°F. Arrange the seasoned duck legs in a single layer onto a rimmed quarter sheet pan, place the duck legs on top, pour ⅓ cup water around the duck legs, making sure not to pour on top, cover the pan tightly with aluminum foil, and bake until the duck is fall-off-the-bone tender, 2 to 2½ hours.  Transfer the cooked duck legs to a plate and set aside (don’t worry if the skin isn’t crispy, you’ll be returning it to the oven later).
4. While the duck is roasting, parboil the potatoes. Place 4 quarts water and 3 tablespoons fine sea salt in a large pot and bring to a boil over high heat. Add the potatoes to the boiling water, cover, reduce the heat to medium, keep at a gentle boil, and cook until the outside of the potatoes is just cooked through, 6 to 9 minutes. Drain and return the potatoes to the hot pot. 
5. Cover with the lid and shake the pot back and forth a few times to rough up the outside of the potatoes. Uncover and set aside.
6. After removing the duck from the pan, increase the heat to 400°F. Pour the rendered duck fat into a container, add 3 tablespoons  back to the pan, and save the rest for another use. Add the parboiled potatoes and the remaining ¼ teaspoon fine sea salt to the pan, gently tossing to coat in the rendered duck fat, and flipping them so they are all cut side down in a single layer. Return to the oven and roast, uncovered, flipping after 25 minutes, until deeply golden and crispy on all sides, 35 to 40 minutes. During the last 15 to 20 minutes, nestle the cooked duck legs in and roast until the skin starts to crisp.
7. While the potatoes are roasting, prepare the salad. Rip the tamarind pulp into smaller pieces, place in a bowl, pour ⅓ cup boiling water over, and let sit for 20 minutes.
8. Meanwhile, heat ¼ cup canola oil in a tadka spoon or small saucepan over medium heat. When the oil is hot, add 24 curry leaves—be careful, these will crackle and pop!—and fry until bright green and translucent, 10 to 30 seconds. Remove the fried curry leaves with a slotted spoon and transfer to a paper towel-lined plate. Add the coriander seeds to the remaining oil off the heat, letting the residual heat toast them, and reserve for later use.
9. To make the dressing, strain the tamarind through a fine mesh strainer into a large bowl, pressing the pulp with a spoon, discarding any leftover fibrous pulp and seeds. Add the lime zest, lime juice, jaggery, and fine sea salt, and whisk to combine. Slowly drizzle in the reserved curry leaf oil-coriander mixture while whisking continuously until all the oil is incorporated and a thick, emulsified dressing forms (it should lightly coat the back of a spoon). Set aside.
10. To prepare the fennel, cut the stalks off the bulbs. Remove the fronds from the stalks and tear into big, bite-sized pieces until you have 1 to 1½ cups fennel fronds. Discard the remaining stems or save for stock. If the outer layer of the fennel bulbs is dry, remove and discard. Using a mandoline or sharp knife, thinly slice the fennel bulbs along with the serrano pepper. (If you want a milder green chili heat, cut the pepper in half, remove the seeds and ribs, and then thinly slice.) 
11. To finish the salad, give the dressing another good whisk to re-emulsify, add the sliced fennel and serrano pepper, and toss to coat. Add the reserved fennel fronds and fried curry leaves, gently toss again, taste, and season with more salt, if necessary.
12. To serve, arrange the duck and potatoes on a platter, leaving room for fennel salad. Pile the dressed salad on the other side of the platter and serve immediately.