Prep ingredients: Trim ends from shallot, then thinly slice half crosswise, separating into rings (save rest for own use) and cut in half baby potatoes. Preheat oven to 425 Degrees
Make curry dressing: In a large bowl, combine curry paste, lime juice, 1 tablespoon water, 11⁄2 teaspoons sugar, and 1⁄4 teaspoon each salt and pepper. Whisk in 3 tablespoons oil. Reserve 1 tablespoon dressing in a bowl for step 6. Toss carrots with remaining dressing in large bowl. Season to taste with salt and pepper. Let stand at room temperature until step 6.
Fry shallots and roast potatoes: Heat 1⁄4 cup oil in a medium skillet over medium-high until shimmering. Add shallots. Cook, stirring, until shallots begin to brown, 2–3 minutes. Remove skillet from heat. Using a slotted spoon, transfer shallots to a paper towel-lined plate. Season with salt. Place potatoes in a oven safe skillet and drizzle with olive. Season with thyme and salt and pepper. Roast for 15 minutes or until potatoes are tender.
Prep pork: Trim excess fat from pork chops to 1⁄4- inch if necessary, then pat dry. Pound to an even thickness if necessary. Season all over with 1⁄2 teaspoon each salt and pepper, pressing gently with your hands to help the seasoning adhere.
Cook pork: Heat 1 tablespoon oil in reserved skillet over medium-high. Transfer pork chops to skillet. Cook until deep golden brown on one side, about 3 minutes. Flip, and cook until browned on the other side, about 2 minutes. Transfer to a cutting board.
Finish & serve: Thinly slice romaine and cucumber crosswise, discarding ends. Toss romaine, cucumbers, and half of each fried shallots. Transfer pork to plates, and drizzle with reserved dressing. Serve with salad and garnish with remaining shallots.