Preheat the oven to 425 degrees F.
In a large bowl, toss the potatoes in the olive oil, and season with a generous pinch of salt and pepper. Arrange the potatoes in a single layer on two baking sheets. Place the sheets in the oven and roast until the potatoes are tender on the inside and crispy on the outside, 40 to 50 minutes.
Place the dried porcinis in a small bowl and fill with boiling water. Rehydrate the mushrooms for 10 minutes. Strain the liquid and chop the mushrooms.
Place the butter in a medium mixing bowl. Add the chopped mushrooms, parsley, thyme, lemon juice and zest, and mix until thoroughly combined. Season with salt and pepper. Reserve 1/4 cup of the butter at room temperature for a later use.
Lay out an 18-inch piece of plastic wrap on a flat surface. Spoon out the remaining butter along the bottom third of the plastic wrap, leaving a 2-inch space on each end. Fold the plastic wrap over the butter and roll it up into a log. Twist the ends to close and roll the tube holding the ends to make sure it's tightly wrapped. Place in the freezer until firm, about 30 minutes.
Remove the plastic and slice half the butter log into 1/2-inch-thick rounds. Place the butter rounds on a serving plate. Wrap the remaining half of the butter log in plastic wrap and store in refrigerator for up to 2 weeks or in the freezer for up to 2 months.
Transfer the potatoes to a large bowl. Add the reserved room temperature butter mixture and toss to evenly coat the potatoes. Serve the potatoes with the extra butter rounds on the side.
You can use baby red bliss potatoes and baby Yukon gold potatoes in place of the tri-color potatoes.