In a bowl, mix together the ricotta, flour, parmesan, eggs, lemon zest and salt. Divide dough into four portions.
Flour a work surface. Working with one portion of dough at a time, roll out the dough into a long rope, approximately 3/4" diameter. Transfer to a cookie sheet. Repeat with the remaining portions.
Place cookie sheet in the refrigerator for 20 minutes.
Using a pastry scraper or a sharp knife, make cuts 3/4" apart down the length of the rope.
In a large saute pan set over medium heat, melt 1 T butter with 1 T olive oil. Add as many gnocchi to the pan as will fit in a single layer without being overly crowded. Cook until the gnocchi has crisped up and is a light golden brown, taking care not to burn them. Flip them over and cook the other side in the same fashion, taking care not to overcook. Remove from the pan to a large serving bowl. Repeat with the remaining gnocchi.
While you are cooking the gnocchi- In a separate small skillet, melt 3 T butter over medium heat. Add the mushrooms to the pan, cooking until they are soft and browned. Add in the asparagus and cook until it softens slightly and is bright green.
Add the garlic and the peas and quickly cook for 1-2 minutes, until the garlic has started to turn light golden and the peas are warmed (but not browning). Add the juice from the lemon that you zested for the gnocchi.
Pour the pan sauce over the gnocchi, then top with 1/3 cup parmesan and 3 T water, tossing all together gently until the cheese has melted and a creamy sauce has formed.
Divide into shallow bowls. Garnish with the chives and serve.