aws-cdk: [cognito] Unable to create user pool with MFA required

(See reproduction steps for code example)

Ideally, I would like to enable MFA required with OTP only (not SMS)

When mfaSecondFactor.sms is set to false, the stack is able to be synthesized, but CloudFormation gives this error:

SMS configuration and Auto verification for phone_number are required when MFA is required/optional (Service: AWSCognitoIdentityProviderService; Status Code: 400; Error Code: InvalidParameterException; Request ID: d5cbb83e-b38a-4f57-9993-65ff923ac325; Proxy: null)

When mfaSecondFactor.sms is set to `true, the stack is not able to be synthesized with the following error:

TypeError: Cannot read property 'uniqueId' of undefined
    at UserPool.smsConfiguration (/Users/barrett/Projects/github.com/tributumtax/monorepo/.yarn/$$virtual/@aws-cdk-aws-cognito-virtual-cef0628d0c/0/cache/@aws-cdk-aws-cognito-npm-1.73.0-8a062b6262-b3bdc35f1d.zip/node_modules/@aws-cdk/aws-cognito/lib/user-pool.ts:884:37)
    at new UserPool (/Users/barrett/Projects/github.com/tributumtax/monorepo/.yarn/$$virtual/@aws-cdk-aws-cognito-virtual-cef0628d0c/0/cache/@aws-cdk-aws-cognito-npm-1.73.0-8a062b6262-b3bdc35f1d.zip/node_modules/@aws-cdk/aws-cognito/lib/user-pool.ts:740:30)
    at new AuthStack (/Users/barrett/Projects/github.com/tributumtax/monorepo/packages/aws/lib/auth-stack.ts:23:22)
    at Object.<anonymous> (/Users/barrett/Projects/github.com/tributumtax/monorepo/packages/aws/bin/aws.ts:45:19)
    at Module._compile (internal/modules/cjs/loader.js:1176:30)
    at Module.m._compile (/Users/barrett/Projects/github.com/tributumtax/monorepo/.yarn/unplugged/ts-node-virtual-9b8834e7f3/node_modules/ts-node/src/index.ts:858:23)
    at Module._extensions..js (internal/modules/cjs/loader.js:1196:10)
    at Object.require.extensions.<computed> [as .ts] (/Users/barrett/Projects/github.com/tributumtax/monorepo/.yarn/unplugged/ts-node-virtual-9b8834e7f3/node_modules/ts-node/src/index.ts:861:12)
    at Module.load (internal/modules/cjs/loader.js:1040:32)
    at Function.external_module_.Module._load (/Users/barrett/Projects/github.com/tributumtax/monorepo/.pnp.js:26436:14)
Subprocess exited with error 1

Reproduction Steps

import { App, Stack, StackProps } from '@aws-cdk/core';
import * as cognito from '@aws-cdk/aws-cognito';

export class AuthStack extends Stack {
  constructor(scope: App, id: string, props: StackProps) {
    super(scope, id, props);

    const userPool = new cognito.UserPool(this, 'UserPool', {
      selfSignUpEnabled: true,
      signInAliases: {
        email: true,
      },
      autoVerify: {
        email: true,
      },
      mfa: cognito.Mfa.REQUIRED,
      mfaSecondFactor: {
        sms: true,
        otp: true,
      },
      passwordPolicy: {
        minLength: 16,
        requireLowercase: true,
        requireUppercase: true,
        requireDigits: true,
        requireSymbols: true,
      },
      accountRecovery: cognito.AccountRecovery.EMAIL_ONLY,
    });
  }
}

What did you expect to happen?

I should be able to deploy the stack

What actually happened?

The synth fails if sms is true and CloudFormation fails if it is set to false.

Environment

• CDK CLI Version : 1.62.0
• Framework Version: 1.62.0
• Node.js Version: 14.2.0
• OS : OS X Catalina
• Language (Version): TypeScript (4.0.20

Other

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This is 🐛 Bug Report