Place a large high-sided pan over medium heat.
Add the olive oil and let it heat up for a few minutes. Then add the shallots and cook undisturbed for 5 minutes, or until they are deeply brown on one side. Flip, add the Fresno peppers, and cook an additional 5 minutes to allow them to caramelize all over.
Season with half a teaspoon of kosher salt and a few cracks of black pepper, and give everything a big stir.
Add in the vinegar and stir to combine. Let the vinegar reduce for 3-4 minutes, or until the shallots are one big sticky pile. Turn off the heat and add 1/4 cup of the basil leaves.
While the balsamic is reducing, pulse together the remaining basil and breadcrumbs in a blender or food processor, until the basil is just flecks in the breadcrumbs.
Place a small pan over medium heat, add the basil breadcrumbs and a drizzle of olive oil and toast for 3-4 minutes or until the breadcrumbs are a shade darker. Season with a pinch of salt and mix.
To serve, scatter the breadcrumbs over the shallots and transfer to a serving dish.