You can make use of the Large Button template. Please see steps below

1. Go to the Core database.

2. Navigate to the path `/sitecore/client/Applications/Launchpad/PageSettings/Buttons`

3. Create or select a section where you want the button to appear.

4. Create a large button based on the template 	`/sitecore/templates/System/Ribbon/Large Button`

5. Fill in the fields.

The main one is the `click` field. This is where you will insert the click event to trigger the powershell script. Example: `item:contextconsole(id=$Target)`

Note that on the Launch Pad there will be no text appearing under the Icon because the template Large Button does not contain the field `Text` which is used to display the label of the icon.

In order to fix this, you can create a template which contain a Text field of type single-line text. Then, the Large button template inherits the newly created template. Once this is done, you can insert a text in the field and this will be shown on the launch pad.

Below is the screenshot of the item in Core database. In this one, I have created the field Text directly on the Large Button template.

[![enter image description here][1]][1]

Then, on the launch pad, the icon is shown under the Content Editing Section

[![enter image description here][2]][2]

**UPDATE**

Based on the test I just performed, when you click on the button, nothing will happen. You will need to use the SPE Web API. Moreover, you will need to add a new field called `link` and then add your rest api in it. Example: `http://hostname/-/script/v2/master/ChildrenAsHtml?item=/sitecore/content&user=admin&password=b`

More information about SPE Web Api can be found here:

- [Configure Web Services][3]
- [Restrict users and roles][4]
- [SPE - Rapid Api][5]


  [1]: https://i.sstatic.net/R5S7J.png
  [2]: https://i.sstatic.net/O2OF1.png
  [3]: https://doc.sitecorepowershell.com/security.html#configure-web-services
  [4]: https://doc.sitecorepowershell.com/security.html#restrict-users-and-roles
  [5]: https://blog.najmanowicz.com/2015/04/13/rapid-api-prototyping-for-sitecore-with-powershell-extensions/