Slice each layer of 12 rolls horizontally, keeping them attached to each other. Set aside.
In a stand mixer fitted with the paddle attachment, beat the cream cheese, sugar and vanilla until soft, 3 to 4 minutes. Scrape down the bowl and paddle with a rubber spatula. Add the cream and beat for 1 minute.
Heat a panini press to 350 degrees F. Lay out half the rolls, the layer with the tops on your left side and the layer with the bottoms of the rolls on your right. Spread half of the cream cheese mixture over the cut sides of the tops, spreading to the edges. Spread about 1/3 cup of the cookie spread on the cut sides of the bottom halves. Sprinkle 1/3 cup of the granola and 1/2 cup blueberries on top of the cookie spread. Place a cube of peach in the middle of each roll. Carefully flip the top of the rolls, cream cheese side down, over the bottom of the rolls. Brush the tops with some coconut oil and sprinkle with some cinnamon sugar. Repeat with the remaining slab of 12 rolls, the remaining cream cheese mixture, cookie spread, granola, blueberries, peaches, coconut oil and cinnamon sugar.
Place one set of 12 rolls in the press and heat until the panini are golden brown and caramelized. (If you can adjust the lid, set it on a wider opening; this will still press the sandwich without squeezing the daylights out of it.) Remove from the press and repeat with the other 12 rolls. The paninis can be made up to 4 or 5 hours ahead and warmed up in a low-temperature oven.
Separate the panini into mini rolls, carefully cutting each slab into 12 pieces. Dust with confectioners' sugar and serve with a side of pure maple syrup, or just by themselves.