Place chiles in a small heatproof bowl and cover with 1 cup boiling water. Let stand until softened, about 5 minutes. Transfer chiles and 1/2 cup liquid to a blender with onion, cumin, coriander, tomato sauce, oil, and 1/2 cup fresh water; blend until smooth. Transfer to a medium saucepan. Bring to a boil, then reduce heat and simmer, stirring occasionally, until thickened slightly, about 15 minutes. Season with salt.
Preheat oven to 350°F. Heat olive oil in a medium skillet over medium. Add onion and season with salt and pepper; cook, stirring occasionally, until soft and translucent, 6 to 8 minutes. Add tomato paste and cumin; cook until fragrant, 1 to 2 minutes. Stir in 1/2 cup enchilada sauce and chicken; cook until warmed through, 1 to 2 minutes. Remove from heat and stir in cilantro and 3/4 cup cheese; season with salt and pepper, to taste. Transfer to a bowl.
Wipe skillet clean and heat vegetable oil over medium-high. Working with one tortilla at a time, add to oil and cook, flipping once, until pliable, 5 to 10 seconds. Transfer to paper towels and pat dry.
Whisk cream into remaining enchilada sauce. Spoon 3/4 cup sauce onto the bottom of a shallow 2-quart baking dish. Place about 1/3 cup chicken filling in the center of each tortilla; roll up tortillas to enclose filling. Arrange enchiladas in a single layer in prepared dish, seam-side down. Pour remaining enchilada sauce over top, then sprinkle with remaining 1/2 cup cheese. Cover tightly with foil.
Bake until sauce is bubbling, about 20 minutes. Uncover and bake until cheese is melted and bubbling, 15 to 20 minutes. Serve with shredded lettuce, sliced chiles, and chopped avocado.