Combine the fish sauce, lime juice, brown sugar, chili garlic sauce, cornstarch, and 1 Tbs. water in a small bowl; set aside. In another small bowl, combine the lemongrass or ginger, garlic, and chile; set aside.
In a 12-inch skillet or wok, heat 1 Tbs. plus 1 tsp. canola oil over high heat. When the oil is shimmering hot, add the carrots. Cook, stirring frequently and making sure to spread them evenly across the pan, until they are browned in spots (some will look charred around the edges, others will have just a few brown spots) and are pliable but still firm, 5 to 6 minutes. Transfer the carrots to a plate and remove the pan from the heat. Let the pan cool for a minute.
Heat the remaining 1 Tbs. oil in the pan over medium-high heat. When the oil is hot, add the shrimp, scallions, and 1/2 tsp. salt. Cook, stirring frequently, until the shrimp are curled up and just cooked through, about 2 minutes. Add the carrots and the lemongrass mixture and stir until very fragrant, about 30 seconds. Add the fish sauce mixture and stir constantly until the sauce thickens slightly, 10 to 20 seconds. Remove the pan from the heat. Stir in half of the almonds and cilantro. Transfer to a serving platter or plates, garnish with the remaining almonds and cilantro, and serve.