Bring a large pot of generously salted water to boiling.
Divide shishito peppers between 3 ounces and 2 ounces. Set aside 2 ounces peppers for later use. Heat a saute pan over high heat, and add olive oil. When the pan is hot, add 3 ounces shishito peppers; cook turning occasionally until blistered in spots. Be careful peppers might pop. Remove from heat.
When peppers are cool enough to handle, , cut to discard the stem and place peppers in container of food processor. Cover and process until finely chopped, scraping the side as necessary. Scrape off the chopped peppers from the container into a bowl.
Crack a whole egg into the bowl of chopped peppers; add egg yolks, heavy cream, Parmigiano-Reggiano, miso, and freshly ground black pepper. Mix everything using a fork until evenly incorporated. The mixture should look like chunky paste.
Add bacon to a saute pan over medium heat; cook until lightly browned and crispy. Remove the bacon and set aside; keep the rendered bacon fat in the pan and add 2 ounces shishito peppers and cook turning occasionally until blistered in spots. Remove the pan from heat.
Meanwhile, add the spaghetti to the boiling water; cook until al dente. Give it stir gently to keep it from sticking if necessary. Reserve some cooking liquid; drain the pasta. Add the spaghetti to the pan; pour the egg mixture and toss everything and stir vigorously with a tong until the sauce becomes creamy and coats the spaghetti evenly. Add splashes of pasta water if necessary. Season to taste with salt. Serve with crispy bacon and freshly ground black pepper on top.