How can my Gradle build initialize class org.codehaus.groovy.classgen.Verifier?

You have to use a more recent version of Gradle:

you can change the distributionUrl to

distributionUrl=https\://services.gradle.org/distributions/gradle-6.4.1-bin.zip

in gradle\wrapper\gradle-wrapper.properties (or wherever your use gradle from in the settings is pointing to).

I've been facing the exactly same issue after installing the latest Kotlin Plugin yesterday. This is what resolved the issue for me: I had to change the version of Gradle used as the build tool to (again) use the version installed on my local system. It seems to me that installing the update has caused my settings to be changed as well.

For doing to open your settings (File -> Settings) and navigate to the Gradle settings (Build, Execution, Deployment -> Build Tools -> Gradle)

There you will see a dropdown for Use Gradle from:. This for me was set to the gradle-wrapper.properties file which it couldn't locate. I changed the selected value to Specified location and ensured that the path which is then displayed is the path to my local Gradle installation. Finally click OK to save the settings.

This is what resolved the issue for me. Hope this helps!

For documentation purposes let me also include the different versions of the tooling on my system (truncated):

IntelliJ IDEA 2020.1 (Community Edition)
Build #IC-201.6668.121, built on April 8, 2020
Runtime version: 11.0.6+8-b765.25 amd64
VM: OpenJDK 64-Bit Server VM by JetBrains s.r.o
...
Non-Bundled Plugins: org.jetbrains.kotlin`

Kotlin Plugin 1.3.72-release-IJ2020.1-1

Gradle 6.3
Build time:   2020-03-24 19:52:07 UTC
...
Kotlin:       1.3.70
Groovy:       2.5.10
Ant:          Apache Ant(TM) version 1.10.7 compiled on September 1 2019