In a medium saucepan, heat 1 tbsp. oil, one turn of the pan, over medium-high. Melt in the butter. Add the rice; stir until golden, 1 to 2 minutes.
Add the stock and saffron; season with salt and pepper. Cover, reduce the heat to low and cook until just tender, shaking the pan occasionally, about 15 minutes. Remove from the heat and let stand 2 to 3 minutes. Fluff with a fork. Add the pimientos and parsley, and toss to combine.
In a large skillet, heat the remaining 1 tbsp. oil, one turn of the pan. Add the chicken and cook, breaking up with a spoon, until browned, about 5 minutes. Add the paprika; season. Stir about a minute. Add the onion and garlic; stir until softened, about 2 minutes. Add the chorizo; cook until heated through, about 2 minutes more. Add the sherry and thyme; stir until evaporated, about 2 minutes. Remove from heat.
If the tortillas are stiff, wrap them in a towel and microwave for a few seconds.
Pile some rice on the lower third of each tortilla, leaving a 2-inch border on either side. Top the rice with the cheese and the chicken mixture. Fold in the sides, then roll up tightly.
Heat a large skillet or griddle over medium-high. Spray the burritos with cooking spray; place in the skillet, seam side down, and cook until crispy and browned, about 2 minutes per side. Cut in half.