For the dressing: Place the minced garlic cloves on a cutting board, then sprinkle with kosher salt. Using the back of your knife, mash the garlic to form a paste. Add it to a bowl with the lime juice, 1/4 cup oil, cumin, turmeric, garam masala and red chile flakes, if using. Whisk together, then season with salt and pepper, if necessary. Remove 3 tablespoons of the marinade and set aside for the squid.
For the squid: Heat up a large grill pan over high heat. Don't put anything on the grill until it's screaming hot! That will prevent the excess sticking.
Meanwhile, place the lemon juice in a large salad bowl and whisk in a pinch of salt and a few grinds of pepper. Add the arugula and toss to lightly coat. Transfer to a serving platter.
Drizzle the nectarine slices with olive oil, and lay them on the grill, turning every minute or so until the fruit have nice grill marks all over. Remove them to a plate. Pat the squid dry with paper towels, if necessary, and add to the reserved marinade. Toss to coat. Shake the calamari of the excess marinade, and place the tubes and tentacles on the hot grill, cooking about 3 minutes per side. If the squid sticks, wait another 30 seconds or so. When it's well-seared, it will release!
Remove the calamari from grill, and slice the calamari tubes (bodies) into rings. Add rings and tentacles to the bowl of reserved dressing and toss well to coat. Arrange the nectarine wedges and calamari on the platter, over the bed of arugula. Drizzle the remaining dressing over the bowl, as desired, and serve.
Combine the cinnamon sticks, cloves, green cardamom seeds, black cardamom seeds, if using in a spice grinder or coffee grinder and grind until fine. Store the spice mix in an airtight container away from direct sunlight.