After struggling with that for several hours, here is my question. I am using CDK to create a VPC in the most simple form currently:
let vpc = new Vpc(this, "myVpc", {maxAzs: 1});
This gets me a public Subnet and a private one with the all the Gateways (internet and NAT). My NAT Gateway got a public EIP from the AWS pool. Of course when i destroy the stack and re-create it, i will get a new EIP from AWS, but THIS i dont want.
What i want is: Creating an Elastic IP outside of my CDK project (manually via CLI or AWS Console) and attach it to my NAT GW, so that even after destroying the stack, i can re-attach my (external) EIP to the "new" NAT GW.
So there must be a way to not have the AWS::EC2::NatGateway created automatically by the VPC but manually with the proper EIP association and then attach it to the VPC / Public Subnet. Pretty much the same way i can explicitly define Subnets and associate them with the VPC instead of CDK construct magic.