How to create a custom template to admin dashboard

Codex has documentation on creating custom login pages – Customize Login Form > Make Custom Login Page, using wp_login_form() function. This should load everything necessary to log user in.

However, unlike login, replacing admin would be much more involved and have many approaches. Typically to access admin function in non-admin context admin PHP files have to be loaded manually which is rather fragile and prone to errors on WordPress version updates.