Working C# equivalent:
public class BaseInterface
{
    public string Name { get; set; }
}

public T getMeObject<T>() where T : BaseInterface, new()
{
    return new T { Name = "WUT" };
}

Not working Typescript:
interface BaseInterface {
    Name: string;
}

function getMeObject<T extends BaseInterface>(): T {
    // {...} cannot be converted into T
    return {
        Name: "omg"
    };
}