Preheat the oven to 400 degrees F.
For the chips: In a large frying pan pour enough oil to fill it 1-inch deep, and heat it to 360 degrees F. When the oil begins to swirl add the tortilla wedges in batches and fry, flipping once until golden and a light tap sounds hollow, about 4 minutes total. Remove to a paper towel-lined plate and sprinkle each batch with a pinch of salt as they are placed on the plate. Transfer evenly to serving plates or a platter.
Meanwhile make the jalapeno salsa: On a baking sheet toss the jalapeno halves, onion, and garlic with olive oil and arrange so that garlic cloves hide under the cavities of the jalapeno halves. Season with salt and pepper, and roast in the oven until the jalapenos begin to blacken and char along with the onions, about 20 to 25 minutes. Remove from the oven and place all the ingredients, oil included, into a food processor. Add the cilantro, chicken stock, and lime juice, blend until smooth, taste and season with salt. Set aside.
For the cheese sauce: In a small saucepan on medium heat, add the butter, oil, onion, pinch salt and couple grinds pepper. Saute until the onions are tender, then add the flour and cook until it stops foaming, but does not brown, about 2 minutes. Add the heavy cream and stir until thickened, about 5 minutes. Add the cheese and stir until melted. Keep warm.
To assemble the nachos, layer the chips on a platter and scatter with the shredded chicken, drizzle cheese sauce, and finish by topping with some of the jalapeno salsa.