Preheat oven to 400°F.
Using a small, sharp knife, trim off the tops and bottoms of both limes. Stand each lime on a cutting board (flat side to the board) and cut down the sides of the fruit, following the curve, to trim away the skin and pith. Discard the skin and pith. Quarter the limes from top to bottom then cut each quarter into thin slices (about 1/8 inch thick). Place slices in a small bowl and sprinkle with a little flaky sea salt. Add 1 tablespoon of olive oil, stirring to combine. Set aside.
Cut the butternut squash in half lengthwise, scoop out the guts (seeds and strings) and discard. Cut each half lengthwise (now you have quarters). Cut the quarters widthwise into 3/8 inch thick slices. Lay the slices on a baking sheet lined with a silpat or parchment paper.
Place several cardamom pods on a cutting board. Using the flat side of a large knife, rest the knife on top of the pods then give it a good thwack with the palm of your hand (be careful here! never hit the sharp part of the knife with your hand). This will allow you to easily get the seeds from the pods. Repeat this process with remaining cardamom pods until you have extracted all of the seeds. Discard the pods.
Place seeds in a mortar and grind with a pestle until you reach a rough powder (or use a spice grinder). Transfer to a small bowl and add allspice and remaining 3 tablespoons of olive oil, stirring to combine. Brush the mixture evenly over the butternut squash slices. Sprinkle the slices with a little flaky sea salt. Place in the oven and cook until fork tender (an inserted fork meets little resistance, about 16 minutes). Remove from the oven and set aside to cool. Once cooled, peel off the skin.
While the squash is cooling, prepare the dressing. Whisk together the Greek yogurt, tahini, lime juice, 2 tablespoons of water and a pinch of flaky sea salt. Continue adding water until the sauce reaches a pourable consistency (I added a few more tablespoons).
To serve, arrange the butternut squash slices on a large platter. Drizzle with yogurt sauce. Spoon over lime slices and their juices. Top with sliced chiles and cilantro leaves.