Preheat the oven to 400 degrees F.
For the compound butter: To a small bowl, add the oregano, thyme, lemon zest, butter and some salt and pepper.
For the roast chicken: Generously rub the outside of the chicken with half of the compound butter, then stuff the cavity with half of the oregano, thyme, lemon and onions. Place the remaining onions and the carrots and celery in the bottom of a roasting pan. Use the rest of the compound butter under the skin of the chicken breasts and legs. Sprinkle the salt and pepper all over the chicken. Place the chicken on top of the vegetables in the pan. Cover with foil and roast for 20 minutes. Then remove the foil and roast until the internal temperature at the thickest part of the thigh registers 165 degrees F on an instant read thermometer, 40 to 45 minutes. Remove the roasting pan from the oven and place on the cooktop. Transfer the chicken to a platter, and allow to rest for 15 minutes. Once rested, remove the stuffing and discard. Shred the chicken, it should yield about 4 cups of shredded chicken.
For the pan gravy: In the roasting pan over medium-high heat, add the flour and stir to combine with the roasting juices. Deglaze with the stock and white wine. Use a wooden spoon to scrape up any of the brown bits on the bottom. Simmer over medium heat. Once the pan sauce reduces by half, remove from the heat. Finish seasoning with salt and pepper. Add the cold butter cubes to the gravy and swirl until melted.
Raise the oven temperature to 425 degrees F. Fill the crepes, one at a time with 2 tablespoons each of chicken and Monterrey Jack cheese. Roll one edge of crepe over the filling then tuck in the sides and continue to roll over so it is seam-side down. Place 5 to 6 crepes in an 8- by 8-inch baking dish with seam-side facing down and cover with more cheese. Place in the oven to melt the cheese, 5 to 7 minutes. Remove from the oven, transfer to a plate and ladle the pan gravy over the top. Whisk the flour, milk, melted butter, salt and eggs together, making sure to remove lumps. Allow to rest for at least 30 minutes.
Place an 8-inch nonstick or crepe pan over medium-high heat and brush lightly with the reserved butter. Spoon 3 tablespoons of the batter into the pan, tilting to evenly coat. Cook until golden brown and flip, 25 to 35 seconds. Transfer to a plate, covering loosely with a kitchen towel and keep warm.