Update 2021-07-21

It's been more than half a decade since I first wrote this answer. The extensions to which I originally linked are abandoned, and Visual Studio Code's intrinsic PHP support hasn't improved, which is disappointing. The only decent extension still standing of which I'm aware is PHP Intelephense, which uses a freemium model: basic features are free, and a lifetime license is $12 USD as of writing.

The free version of Intelephense supports code formatting with the usual shortcuts (Alt + Shift + F on Windows and Linux, ⌥⇧F on macOS). Visual Studio Code continues to lack built-in support for PHP code formatting and will direct you to the extension marketplace if you attempt to format PHP without an appropriate extension installed.

Original answer

Visual Studio Code has pretty awesome PHP support. What it lacks is covered by extensions. A quick search reveals at least three (1, 2, and 3) that claim to support PHP formatting.

They mostly seem to use the standard shortcut of Alt + Shift + F on Windows/Linux, with varying shortcuts on Mac. If you're on Mac, give ⌥⇧F a try.

The extension Beautify (from HookyQR) just does it very well. Either add PHP, and any other file extension type, to the configuration. As said by Nico, here is an example:

1. Go to user settings (Ctrl + Shift + P → User settings (UI) or Ctrl + , (comma)

2. Search for Beautify in the field above. And click on "Edit in settings.json" for "Beautify: Config".

3. For the "html" section, add "php" and "blade".

   

###Usage

You can invoke it directly. Press F1, and then write Beautify. The auto completion gives you two choices, "Beautify file" and "Beautify selection". Choose the one you need, and it will do the job. That's a straightforward direct way.

You can also add a keybinding to have a keyboard shortcut. Here is how to do it:

1. Open keybindings.json (go to menu File → Preferences → Keyboard Shortcuts)

2. Click in the above. Open and edit file keybindings.json

3. Add the following into the closed brackets, []

   {
          "key": "alt+b",
          "command": "HookyQR.beautify",
          "when": "editorFocus"
   }
   

   Choose any key you want, and make sure you don't override an existing one. Search first in the left side if it exists or not.

   

Note that all of those things are well documented in the description of the extension.

Extra: Note about blade

(suite to @Peter Mortensen clarification pinpoint)

blade or blade.php

If you are confused if it's blade or blade.php for the setting! I'll clear it up for you! It's blade! That's vscode keyword for the language!

How do you know ?

First if you open the list of languages as by the image bellow:

Write blade

You can see Laravel Blade (blade)! The language keyword is in the paratheses! blade!

Well but how to check!

Try with blade.php in the settings!

Try to beautify

You'll get an asking context menu for what language (html, css, js)!

So it doesn't works!

To really know ! Put back blade! And it will work and beautify directly!

How well it works with blade

The awesome answer to that! Is try it, and see for yourself!

But if you ask me! I'll say it does work as with html! It can be too handy! And you may need to fix some lines! Depending on your expectations and your style!

Here an illustration! I screwed the indentation in purpose

And here the beautification result:

Luckily I felt the same way as you so I just decided to go ahead and hammer out a solution to this very annoying problem with a VScode extension that doesn't register itself as a "formatting" extension I format the HTML onBeforeSave so you can still register a PHP formatting extension so between the two it gets the whole file. I use js-beautify so you can just use all the native HTML formatting settings in VSCode already.

Format HTML in PHP on the VSCode Extension Marketplace.

There are many extensions in the marketplace of VSCODE for formatting the code. Try one of them. I might even recommend Prettier ext. Try others as well you might one usefull