Suppose one has ~300000 JPY in cash. In the Netherlands, what is the cheapest way to convert this cash to EUR, and send it to an account?
When you have the money electronically, you can use cheap transfer / conversion services like OFX / XE / Transferwise or the newer Revolut app.
If you have physical cash, your options are more limited.
For physical cash, the cheapest you can usually get is to find someone who is traveling to Japan soon or frequently travels to Japan and exchange the cash directly with them. For 300000 JPY, it's probably best to find someone you already know well to minimize your risk of telling someone else that you will have a large amount of cash on you.
However, your most likely bet is to check conversion rates (including fees) at a bank branch and also at a currency exchange location and pick the one that has the best conversion rate. Note that most banks in the Netherlands no longer convert foreign currency. ABN AMRO does but only in Schiphol. Most others direct you to GWK Travelex. You may be able to find a smaller bank that still does this. For currency exchange offices, the major train stations like Amsterdam Centraal, Rotterdam Centraal, Utrecht Centraal, etc all have a GWK Travelex office. Schiphol has more options, including the ABN AMRO offices dedicated to currency exchange.