Fill the bottom of a medium saucepan with water. Insert a steamer basket, add the broccoli, cover with a lid, raise the heat to high and steam the broccoli until it is vibrant green and slightly fork-tender, around 5 minutes. Remove the broccoli from the heat and let it cool before roughly chopping it into small pieces.
In a large bowl, combine the chopped broccoli, grated Dubliner cheese and diced roasted bell peppers. Toss to incorporate and refrigerate 15 minutes.
In a separate bowl, combine the onion powder, garlic powder, paprika, Italian seasoning, salt and pepper. Stir to incorporate.
Using a sharp knife, butterfly the chicken breasts lengthwise, making sure to stop just before slicing through the opposite side. Open the chicken breast like a book and place it between two pieces of parchment paper. Pound the chicken breasts until they are roughly 1/2” thick using a meat mallet, rolling pin or frying pan.
Preheat your Traeger Grill or oven to 400F.
Lightly season the insides of each chicken breast with the spices and equally stuff with the cheese mixture. Fold over the top of each chicken breast, pushing any loose filling towards the centre and secure the edges with toothpicks or skewers. Massage each chicken breast with a small amount of olive oil and season both sides with the spices.
Preheat a large, oven-safe frying pan over medium-high heat. Add 3 tablespoons of olive oil and heat until shimmering. Add the chicken breasts and cook, undisturbed, until golden brown, around 6 minutes. Flip the chicken and transfer the pan to the oven. Cook until the thickest part of the chicken registers 160F, around 12 minutes. Reserve any drippings in the pan, transfer the chicken to a plate and loosely tent it with foil to keep warm.
Set the pan with drippings over a medium heat, add the garlic and cook, stirring, until fragrant, around 1 minute. Add the chicken broth and cook, lifting any brown bits off the bottom of the pan, until the liquid has reduced in volume by ¼, around 3 minutes. Add the lemon juice and Calabrian chili paste and cook, stirring to incorporate, for 1 minute. Add the butter and cook, stirring, until emulsified. Add the basil and parsley and stir to incorporate. Taste the sauce for seasoning and adjust with lemon juice or chili paste as desired.
To serve, place the chicken breasts onto individual serving plates and remove the skewers. Top the chicken with the Calabrian chili sauce and serve with a side of mixed greens dressed with a drizzle of olive oil and lemon juice.