1. Pulse chiles, 4 shallots, and garlic in food processor until coarse paste is formed, about fifteen 1-¬second pulses, scraping down sides of bowl as necessary. Transfer mixture to small bowl and set aside. In second small bowl, stir together brown sugar, molasses, soy sauce, fish sauce, and 1 1/4 teaspoons salt. Whisk eggs and 1/4 teaspoon salt together in medium bowl.

2. Thinly slice remaining 3 shallots and place in 12-inch nonstick skillet with oil. Fry over medium heat, stirring constantly, until shallots are golden and crisp, 6 to 10 minutes. Using slotted spoon, transfer shallots to paper towel-lined plate and season with salt to taste. Pour off oil and reserve. Wipe out skillet with paper towels.

3. Heat 1 teaspoon reserved oil in now-empty skillet over medium heat until shimmering. Add half of eggs to skillet, gently tilting pan to evenly coat bottom. Cover and cook until bottom of omelet is spotty golden brown and top is just set, about 1 1/2 minutes. Slide omelet onto cutting board and gently roll up into tight log. Using sharp knife, cut log crosswise into 1-inch segments (leaving segments rolled). Repeat with another teaspoon reserved oil and remaining egg.

4. Remove rice from refrigerator and break up any large clumps with fingers. Heat 3 tablespoons reserved oil in now-empty skillet over medium heat until just shimmering. Add chile mixture and cook until mixture turns golden, 3 to 5 minutes. Add shrimp, increase heat to medium-high, and cook, stirring constantly, until exterior of shrimp is just opaque, about 2 minutes. Push shrimp to sides of skillet to clear center; stir molasses mixture to recombine and pour into center of skillet. When molasses mixture bubbles, add rice and cook, stirring and folding constantly, until shrimp is cooked, rice is heated through, and mixture is evenly coated, about 3 minutes. Stir in scallions, remove from heat, and transfer to serving platter. Garnish with egg segments, fried shallots, and lime wedges; serve immediately.