Tip:Seasoning with salt at the end of the cooking process may seem unconventional, but it actually works better in stir-fries. Salt encourages vegetables to break down and release water, and that is not the goal in these dishes.
Toast 1 tsp. of the cumin seeds in a small skillet over medium-high heat, stirring frequently, until deeply browned and beginning to smoke, 3 to 5 minutes. Transfer to a bowl to cool. Grind to a fine powder in a spice grinder.
Heat the oil with the remaining 1/2 tsp. cumin seeds, the coriander, and peppercorns in a large wok, Dutch oven, or 12-inch skillet over medium-high heat, and cook until the cumin is browned, about 2 minutes. Add the jalapeño and cook until sizzling and just starting to soften, 30 to 60 seconds, and then add the cabbage and carrots. (If using a skillet, the pan will be crowded at first.) Cook, stirring occasionally until the cabbage has wilted yet is still al dente, 3 to 4 minutes. Stir in the freshly ground cumin, salt, and sugar, and cook for 30 seconds. Remove the skillet from the heat. Stir in the cilantro and lime juice and taste for seasoning. Serve warm, at room temperature, or cold.