Yes, you can. Have a look at the ArduinoBLE library examples. There are examples for Central/client and Peripheral/server.
The peripheral/server is usually the low power node e.g. a heart rate sensor and the central/client usually has more power available and initiates data transfers and analyses/displays the data e.g. a smart phone but can be another Arduino as well.
From an application layer point of view the server creates a service with characteristics and stores new data in it when ever the application has new data. The server never sends the data without a request.
The client uses the GATT protocol to read what data is available. The data can have read and/or write access.
Start with the server and uses a smartphone with a generic BLE app. I use BLE Scanner on iPhone. Have a look at the source and the data you can read in the app.
Then you can use a central app to read the data from the server.