Is there a way to set up a recurring or scheduled expense that is billed the same each month?
Recurring contract types are designed to bill same amount at a set frequency. All you need to do is set up a project with recurring contract type and enter the amount and frequency. Core then generates invoices automatically for that amount and frequency. Check the Core Help for details.
Another option is Automatic Billing wherein you can just set the billing frequency on the project and it will generate the invoice automatically based on the contract type, billing schedules, and billable time and expenses. This automatic billing is dynamic because of the changing bill amount. Check the Core Help for details.
Automatic billing differs from memorized billing as that is set at the project level while the latter is set at the invoice level. Unlike automatic billing for a project with variable bill amount, in case of recurring billing, you have a pre-defined fixed amount being invoiced to the client, irrespective of the work done on projects.