The Community Digests feature seems like it could more or less fit this purpose for you; it's a weekly email that contains both new and old highly-rated questions from a specific Stack Exchange community/ site.
They have 3 sections, the second of which sounds most applicable: "Top new questions this week", "Greatest hits from previous weeks", and "Can you answer these questions".
You can subscribe to any site's digest and see previews of what they look like via https://stackexchange.com/digests.
You can also see and manage existing subscriptions to newsletters from your user settings at https://meta.stackexchange.com/users/email/digests/current.