Prep: Clean and cut leeks into ¼ inch thick half-moons (step-by-step instructions here).
Base: Heat oil in a large pot over medium heat. Add leeks and garlic, cooking leeks are a bit soft and bright green, about 7 minutes. Remove half of the leeks and save for later, leaving the other half in the pan.
Rice: Add dry rice to the pan and cook for about 2 minutes, stirring frequently, until the rice is slightly opaque on the outside but uncooked on the inside.
Liquids: Add wine to the pot and simmer until absorbed. Slowly add the vegetable broth, adding ½ cup at a time. Wait until broth has almost completely absorbed before adding another ½ cup. Begin tasting the rice after 15 minutes or so. Once it is al dente (a little bit chewy), stop adding broth (you may not need the full amount).
Add-Ins: Stir in parmesan until melted. Stir in frozen peas, goat cheese, and reserved leeks. Taste and add salt, pepper, and lemon juice to suit your taste.
Video
Notes
For strict vegetarians, look for a vegetarian parmesan brand (you can often find it at Whole Foods and health food grocery stores).