Add potatoes to a large pot of cool salted water. Bring water to a boil and cook for 20-25 minutes, or until fork can easily pierce potato. Drain potatoes and set aside until cool enough to handle but warm.
Remove skin from potatoes. In a medium bowl, mash potatoes until all lumps are gone. Add salt and pepper and mix well. Make a well in the center of potatoes and crack an egg into it. Whisk eggs briefly. Then, using your hands, gently mix it into potatoes until evenly distributed.
Put 1 cup of flour onto a clean surface and turn out potato dough onto it, keeping the remaining 1/2 cup close by in case you need to add extra. Working quickly and carefully, knead dough, only adding as much flour until dough loses stickiness and becomes more solid. Slice dough into 4 parts. Roll out 1 part into a long rope, about 1 inch wide, cutting in half and working with 1 half at a time. Slice rope into 1/2-inch squares and set aside on a lightly floured surface. Repeat with remaining dough.
Bring a large pot of salted water to a boil and add gnocchi in small batches, stirring gently to ensure they aren't sticking. Boil until they float to the surface; after another 15-30 seconds in the water, remove.
In a pan over medium heat, melt butter and add sage. Add gnocchi and toss until lightly golden.
Serve with warm pesto or marinara sauce and garnish with cherry tomatoes and green basil.