Adjust an oven rack to the middle position, place a rimmed sheet pan on top, and preheat the oven to 375° F.
Toss the shallots with the olive oil, cumin, thyme, 1 teaspoon salt, and the pepper in a large bowl. Turn the shallots out onto the heated sheet pan in an even layer and cook until they brown, about 25 minutes.
Wearing oven mitts, pull the oven rack out halfway and stir the lentils into the shallot mixture on the sheet pan. Carefully add the boiling water and cover the sheet pan with aluminum foil (you may need 2 sheets), crimping it around the edges to seal. Reduce the oven temperature to 350° F and bake for 10 minutes.
Pull the rack out partway again, open the foil and stir in the rice and remaining 1 ½ teaspoons salt. Re-cover the sheet pan, crimping the foil around the edges to seal, and continue to cook until the rice is tender, about 25 minutes more.
Remove the pan from the oven. Taste and adjust the salt if needed. Sprinkle with the parsley or cilantro, dress with yogurt, Aleppo-style pepper, and additional olive oil, and serve warm or at room temperature.