title: ESLint not reporting TypeScript compiler type checking errors
body: <p>Looking for help in getting the type errors, reported by the TypeScript compiler, into the output of ESLint. The library typescript-eslint (<a href="https://github.com/typescript-eslint/typescript-eslint/blob/master/docs/getting-started/linting/TYPED_LINTING.md" rel="noreferrer">https://github.com/typescript-eslint/typescript-eslint/blob/master/docs/getting-started/linting/TYPED_LINTING.md</a>) makes me think that this should be possible.</p>
  
  <p><strong>File structure</strong></p>
  
  <pre><code>src/
    ... source files
    tsconfig.json
  test/
    ... testing files
  .eslintrc.js
  package.json
  tsconfig.json (symlink to src/tsconfig.json)
  </code></pre>
  
  <p><strong>.eslintrc.js</strong></p>
  
  <pre><code>module.exports = {
    'env': {
      'jest': true,
      'node': true,
    },
    'extends': [
      'airbnb-typescript/base',
      'plugin:@typescript-eslint/eslint-recommended',
      'plugin:@typescript-eslint/recommended',
      'plugin:@typescript-eslint/recommended-requiring-type-checking',
      'plugin:jest/recommended',
    ],
    'parser': '@typescript-eslint/parser',
    'parserOptions': {
      'project': ['./tsconfig.json'],
      'tsconfigRootDir': __dirname,
    },
    'plugins': [
      '@typescript-eslint',
      'jest',
    ],
    'root': true,
  };
  </code></pre>
  
  <p>package.json</p>
  
  <pre><code>{
    "name": "...",
    "version": "...",
    "description": "...",
    "scripts": {},
    "devDependencies": {
      "@types/jest": "^25.1.3",
      "@typescript-eslint/eslint-plugin": "^2.21.0",
      "@typescript-eslint/parser": "^2.21.0",
      "eslint": "^6.8.0",
      "eslint-config-airbnb-typescript": "^7.0.0",
      "eslint-plugin-import": "^2.20.1",
      "eslint-plugin-jest": "^23.8.1",
      "jest": "^25.1.0",
      "nock": "^12.0.2",
      "ts-jest": "^25.2.1"
    },
    "dependencies": {
      "@types/node": "^13.7.7",
      "aws-sdk": "^2.630.0",
      "jsonschema": "^1.2.5",
      "typescript": "^3.8.3"
    }
  }
  </code></pre>
  
  <p>The output of ESLint is empty - no errors - but when running the TypeScript compiler, to build the project, there are many errors reported; for instance:</p>
  
  <pre><code>src/file.ts:xx:xx - error TS2339: Property 'body' does not exist on type 'object'.
  src/file.ts:xx:xx - error TS2314: Generic type 'Promise&lt;T&gt;' requires 1 type argument(s).
  src/filets:xx:xx - error TS7006: Parameter 'err' implicitly has an 'any' type.
  </code></pre>
  
  <p>Am I missing something in the configuration or is it improper in some way? Or is this not something that is actually possible?</p>
  
  <p>I'd like to get the errors reporting through ESLint because I have the linting errors showing in my editor as I work on the project. I am using Atom (<a href="https://atom.io/" rel="noreferrer">https://atom.io/</a>) but I would also like this to work for VSCode and possibly VIM as well; team members prefer different editors.</p>