Heat the olive oil in a pan over medium heat. Add the banana peppers (and optional hotter chili) and cook 5-7 minutes, stirring often, until softened and lightly browned.
Add the garlic and cook 1/2-1 minute, until fragrant.
Add the vinegar, water, sugar, and salt. Bring to a simmer and cook 10 minutes.
Cool slightly, then transfer to a blender and blend until smooth. Stir in fresh lime juice.
Taste and adjust for salt, vinegar, and lime. Add more water or vinegar for a thinner sauce. Strain if desired.
Pour into bottles or a jar. Cool completely before sealing, then refrigerate.