Bring stock to a simmer in a large pot. Meanwhile, in a food processor, purée 1 cup peas with 1 cup water.
In a large saucepan, heat oil over medium heat, add onion and cook until softened. Add rice and toast for 1 minute.
Add 1/2 cup Riesling and simmer until liquid is almost evaporated.
Add just enough stock to cover the rice, then let simmer until it’s just about absorbed.
Continue adding stock in this manner, stirring with each addition, until rice is al dente and has formed a creamy sauce.
Stir in pea purée and remaining peas (and bacon, if using); stir until heated through.
Remove from heat; stir in butter, cheese and lemon juice. Taste and season with salt and pepper as needed.
Pour enough Riesling in a separate wide, shallow saucepan to reach a height of about 2 inches.
Bring to a simmer, then gently lower eggs in and cook over a bare simmer until poached, about 4 minutes.
Divide risotto among serving plates and top each with a wine-poached egg. Season again with salt and pepper, sprinkle with chives if desired and serve immediately.