Heat the oven to 350°F. Cook mushrooms in oil in a wide skillet over medium-high heat for 10 to 12 minutes until browned and their liquid evaporates.
Add garlic and stir for 30 seconds, then add spinach in handfuls with salt and pepper. Cook for 3 to 4 minutes until wilted and the skillet is dry.
Split the connected Hawaiian rolls horizontally and put the bottom slab in a parchment-lined 9-by-13-inch pan. Spread with Dijon and layer on half the Havarti, vegetables and remaining cheese.
Replace the tops, brush with butter and cover with foil. Bake for 15 minutes, then uncover for 8 to 10 minutes until the center reaches 165°F.
Rest for 5 minutes and cut into 12 sliders.