Bring Queen Green lentils, 5 cups water, and 1/2 tsp salt to a boil in a heavy medium saucepan, then simmer, uncovered, until lentils are just tender, 20 to 25 mins. Drain, then transfer to a large bowl.

Meanwhile, cook 1 tsp garlic in 1 tbsp oil in another heavy medium saucepan over medium heat for 1 min, stirring. Add rice and cook, stirring, for 1 min. Add remaining 2½ cups water and 1 tsp salt and bring to a boil, then cook, covered, over low heat 20 mins. Remove from heat and let stand, covered, 10 mins. Stir rice from top to bottom with a rubber spatula, then stir into lentils.

While rice stands, sauté onion and remaining garlic in 1 tbsp oil in a heavy nonstick skillet over medium-high heat until onion is golden, 3 to 5 mins. Stir in chile paste and cook, stirring, 1 minute. Stir onion mixture into rice mixture.

Heat remaining ¼ cup oil in skillet over medium heat until hot. Add rice mixture and fry, gently flattening with a spatula, until a golden-brown crust forms on underside, about 3 mins. Stir rice and fry, flattening it, until a crust forms on underside again, about 3 mins more. Repeat frying and stirring until bits of crust are dispersed throughout, about 9 min more (about 15 mins total frying time).