Place medium-sized sauce pan on low heat, add olive oil, shallots, and garlic. Lightly sauté for 60 seconds until slightly translucent.
Turn heat up to medium and add cherry pepper, sauté for 30 seconds.
Add fresh lemon juice and reduce by 1/2 in volume, about 45 seconds to 1 minute.
Add white wine and turn up heat to medium-high heat, reduce to 1/3 in volume about a minute.
Add chicken stock and reduce to 1/3 in volume about 2 to 3 mins.
Turn off heat and whisk in cold unsalted butter and chopped dill until emulsified and sauce-like. Season to taste with salt and pepper.
Serve warm immediately.