First of all, check here whether an EORI number has already been allocated. The EORI number is derived from the VAT number. This means the VAT number can be entered on this site, without B01.
There are 2 application forms on this page of the Dutch tax authorities; one for companies headquartered in the Netherlands looking to apply for an EORI number and one for companies which have their headquarters outside the European Union.
TAKE NOTE! It is important that the form is filled in digitally. In addition, an EORI number cannot be issued to a tax entity, but it can be issued to the underlying entities. Furthermore, the company must be of valid legal status as well.