Prepare a large pot of salted water to cook the pasta; begin to heat the water over low heat. In a small saute pan, heat 1 ½ tablespoons Lucini extra virgin olive oil, add crushed garlic and the peas. Saute for a few minutes until the peas are cooked; add a little salt and set aside.
Put the 3 tablespoons of extra virgin olive oil, minced garlic and diced red pepper in a frying pan over medium heat (add the hot pepper, if using).
Sauté for about 5 minutes, then add the chopped parsley, continue to cook for about 30 seconds, then add the chicken stock. (Can I tell you that the aroma that will fill your kitchen, at this point, is reason enough to make this recipe!)
Let simmer over high heat, until the liquid is reduced by about half; then add the cream and continue to cook for 3 to 4 minutes.
At this time, bring the water to a rolling boil, then add the bucatini. Cook for 7 minutes, as directed on the package.
After the cream sauce has thickened, add the butter, swirling the pieces into the sauce, until completely melted. Taste the sauce and add salt, if needed, and some white pepper.
Remove from heat. Transfer the red peppers and cream sauce to deep container, and create a smooth sauce by using an immersion blender (traditional blender may also be used.)
Drain the pasta; return to the pot. Add the peas and sauce, and stir to combine evenly. Garnish with chopped parsley, or sprigs of parsley, and serve immediately.