Partez l'esprit tranquille en vacances en nous laissant nous occuper de votre installation.
On several separate occasions, I have heard native French speakers around me use the phrase « l'esprit tranquille » like an adverb. It rubbed off on me, and now I use it in conversation myself.
The thing is, I would expect some additional word like « avec l'esprit tranquille » to make it grammatically correct. I wonder if « l'esprit tranquille » is an exceptional case where a noun phrase is used like an adverb? Or are there other similar expressions?