I have an ASP.NET Core website, using EFCore. I would like to do some work like logging to the database, but after having sent the response to the user in order to answer faster
Try using Hangfire. Hangfire is an easy way to perform background processing in .NET and .NET Core applications. No Windows Service or separate process required. Backed by persistent storage. Open and free for commercial use.
You could do something like
var jobId = BackgroundJob.Enqueue(() => Log(model));
And here is my blog post on using HangFire in ASP.NET Core