Preheat oven to 350 degrees. Line a baking sheet with parchment paper and set aside.
In a small saucepan, over low heat, warm milk and 3 tablespoons of butter until butter is melted and mixture is between 100-115 degrees. Whisk in sugar and yeast and let stand until the yeast is dissolved and starting to foam, approximately 10 minutes.
Beat 1 Eggland’s Best egg and add it to milk mixture, stirring constantly until well combined.
Using a hand mixer or stand mixer fitted with the dough hook attachment, mix flour and milk mixture on low speed until all ingredients are combined.
Increase speed to medium for approximately 1 more minute. Add salt and mix at medium speed for approximately 4-5 minutes, or until dough comes off the sides of the bowl and forms a uniform ball.
Lightly coat dough with cooking spray and wrap loosely in plastic wrap.
Place in a warm area and let dough rise until it has doubled in size, approximately 1 ½ hours.
While dough is rising, chop ramps into small pieces and set aside. Slice mushrooms into ¼-inch size pieces.
Heat a large skillet and add 1 tablespoon to melt over medium heat. Add ramps and mushrooms and saute until golden brown and ramps are starting to wilt.
When finished, drain and set aside.
When dough is ready, turn out on well-floured work surface. Divide dough into 8 equal parts.
With the heel of your hands, flatten dough into a rectangle shape, adding a little flour if the dough is still sticky.
Sprinkle cheese into the center of the dough. Add 7 7 slices of pepperoni, and top with 1-2 tablespoons of mushroom mixture. Do not overfill.
Gather the sides of the dough and bring them towards the center. Take the dough side closest to you, tuck all ingredients under and roll it all, like a burrito. Place seam side down on a baking pan with parchment paper. Make sure the seam is tightly closed and repeat until all ingredients are used.
When rolls are assembled, spray each top very lightly with cooking spray and lightly wrap pan with.
When all are done, spray the tops of the rolls, lightly plastic wrap the rolls and pan and place back into the warm area for another 15-20 minutes.
Whisk 1 egg and water together and brush tops of each roll before baking. Place in oven and bake for 20 minutes, rotating halfway through, or until golden brown.
Allow to cool for 10 minutes before serving.