Cypress + Typescript ts-loader option `transpileOnly` config helps with memory-contrained machines if you're not running in the Cypress Dashboard but rather using custom Jenkins CI, etc.

index.js

module.exports = (on, config) => {
  // ...
  
  const wpOptions = webpack.defaultOptions
  wpOptions.webpackOptions.resolve = {
    extensions: ['.ts', '.js'],
  }
  wpOptions.webpackOptions.module.rules.push({
    test: /\.ts$/,
    exclude: [/node_modules/],
    use: [
      {
        loader: 'ts-loader',
        options: {
          transpileOnly: true, // https://github.com/TypeStrong/ts-loader#transpileonly-boolean-defaultfalse
        },
      },
    ],
  })

  on('file:preprocessor', webpack(wpOptions))
  
  // ...
}

@chiptus I don't think this is an issue anymore using recent versions of Cypress, at the time this was a problem in v2 and v3. If that is what you're stuck on, yes you would need to import webpack somehow.