I went through the Toolbar
source code to find a solution and it turned out to be pretty simple.
Toolbar uses two styles to style the toolbar and the navigation icon. Just had to override those styles with my own.
<style name="myToolbarNavigationButtonStyle" parent="@style/Widget.AppCompat.Toolbar.Button.Navigation">
<item name="android:minWidth">0dp</item>
<item name="android:padding">12dp</item>
<item name="android:scaleType">centerInside</item>
</style>
<style name="myToolbarStyle" parent="@style/Widget.AppCompat.Toolbar">
<item name="android:paddingRight">10dp</item>
</style>
<style name="AppTheme" parent="AppBaseTheme">
<item name="toolbarStyle">@style/myToolbarStyle</item>
<item name="toolbarNavigationButtonStyle">@style/myToolbarNavigationButtonStyle</item>
</style>
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