Heat the oven to 350°F. Heat oil in a large skillet and cook chicken with salt for 9 to 11 minutes, stirring, until the pieces reach 165°F. Drain watery liquid.
Stir hot sauce and 1 tablespoon butter into the hot chicken. Split the connected Hawaiian rolls horizontally and set the bottoms in a parchment-lined 9-by-13-inch pan.
Layer on Monterey Jack, chicken and blue cheese, then replace the top slab. Melt the remaining 3 tablespoons butter and brush over the tops.
Cover with foil and bake for 15 minutes, then uncover for 8 to 10 minutes until the filling reaches 165°F.
Rest for 5 minutes, lift the top slab carefully and scatter diced celery over the chicken. Replace the top, cut into 12 sliders and serve promptly.