To make the relish, combine the poblano, Hatches, Serrano, vinegar, honey, olive oil and cilantro in a bowl and season with salt and pepper. Let sit at room temperature for at least 30 minutes before serving. The relish can be made 1 day ahead in advance and refrigerated; bring to room temperature before serving.
To cook the burgers, heat a griddle or a large sauté pan over high heat. Add the canola oil and heat until it begins to shimmer.
Divide the meat into 4 equal portions. Form each portion loosely into a 3/4-inch thick burger and then make a deep depression in the center with your thumb. Season both sides of each burger with salt and pepper. Cook the burgers until golden brown on both sides and cooked to medium, about 8 minutes.