Preheat oven to 300 degrees F. In the jar of a blender, add the white onion, ancho chile powder, tomato paste, salt, Mexican oregano, dried thyme, dried marjoram, juice from 1 lemon, beer and chicken stock; pulse until smooth.
Place the chicken in a 8x8-inch casserole dish. Pour the tomato mixture atop the chicken; the chicken should be mostly covered--it's ok if their tops are peeking out of the sauce. Transfer to the oven to bake for 1 1/2 hours, until just cooked and chicken is tender. Allow the chicken to cool on the counter until they're cool enough to handle. Using a fork, shred the chicken. Toss the chicken with a few tablespoons of the tomato mixture from the casserole dish.
To warm the tortillas, stack them on a microwave-proof plate and cover them with a damp paper towel. Warm them for 20 seconds or until pliable. If you're without a microwave, you can do this in the oven, too. Turn the oven to 200 degrees F, place the tortillas, stacked, on a baking sheet and cover them with a damp paper towel; transfer to the oven to warm for 10 minutes.
In a medium skillet, pour in enough oil until it reaches about 1/2-inch up the sides of the pan. To assemble the taquitos, spoon a few tablespoons of the chicken mixture onto the lower third of each tortilla. Tightly roll up each taquito and transfer to the hot oil, seam-side down. Pan-fry the taquitos for 2 to 3 minutes, turning them every so often, until they're golden brown and crispy. Drain the taquitos on a bed of paper towels and transfer them to a baking sheet in a warm oven (200 degrees F). Repeat the stuffing and pan-frying process until you've cooked up all of the taquitos.
To make the avocado creama, add all of the ingredients to a food processor and pulse until smooth. (If you don't have a food processor, you can also do this in a bowl, no biggie!) Serve the taquitos with a dollop of avocado crema, a sprinkling of cotija cheese and sliced radishes.