In a medium saucepan, combine the diced bell pepper, minced chili and jalapeño peppers, garlic, apple cider vinegar, salt, ground mustard, and black pepper.
Bring the mixture to a boil over medium-high heat. Once boiling, reduce the heat to low and let it simmer for 15-20 minutes, stirring occasionally. The peppers should soften, and the liquid should reduce slightly.
Taste the relish and adjust seasoning as needed (e.g., more salt for flavor or a touch of honey if you prefer a sweeter balance).
Remove the cooked mixture from the heat and let it cool slightly. Transfer to a food processor or blender and blitz until your desired texture is reached. For a chunky texture, pulse a few times; for a smooth consistency, process longer.