If I’m trying to deploy a new image with a specific version, should I do something like this:

const version = require('../../apps/service/package.json').version;
...
const image = new awsx.ecr.Image(`image:${version}`, {
  repositoryUrl: repository.url,
  path: "./app/service/",
});

Or is there a different way to specify the version on the image?

awsx.ecr.Image

is designed to build the image locally for you and push it. If the image already exists in the ECR repo and you know the image tag, just specify that in your task definition

Is there some way of having the image be tagged with a specific version? Specifically I want to be able to "roll back" to a previous version without going through a build process

not with

awsx.ecr.Image

no, it auto generates an image tag for you. If you want more control over the image and the process of building/pushing, you likely want to use https://www.pulumi.com/registry/packages/docker/api-docs/image/ which allows you to set a tag in the image name. It’s worth pointing out though, Pulumi drives towards a desired state, so with this:

Specifically I want to be able to “roll back” to a previous version without going through a build process

You’ll probably want to just modify the task definition and do your docker image builds outside Pulumi