Custom content allows you to open an overlay panel instead of a menu.
Source
<p:badge value="1" severity="danger">
<pe:fab id="btnFab" icon="pi pi-question-circle" iconActive="pi pi-times" style="background: green;" widgetVar="fabWidget">
<pe:javascript event="open" execute="PF('overlayWidget').show('btnFab');"/>
<pe:javascript event="close" execute="PF('overlayWidget').hide();"/>
</pe:fab>
</p:badge>
<p:overlayPanel id="overlayPanel" widgetVar="overlayWidget" appendTo="@(body)" showEffect="drop" hideEffect="slide">
<p:panelGrid styleClass="ui-noborder">
<p:row>
<p:column styleClass="ui-widget-header">
<p:outputLabel for="txtMessage" value="Message"/>
</p:column>
</p:row>
<p:row>
<p:column>
<p:inputTextarea id="txtMessage" rows="5" cols="43" autoResize="false"/>
<p:watermark for="txtMessage" value="Send us a message if you have something to say."/>
</p:column>
</p:row>
<p:row>
<p:column styleClass="ui-widget-header">
<p:outputLabel for="txtEmail" value="Email address (optional)"/>
</p:column>
</p:row>
<p:row>
<p:column>
<p:inputText id="txtEmail" size="40"/>
<p:watermark for="txtEmail" value="Email address (optional)"/>
</p:column>
</p:row>
<p:row>
<p:column style="font-style: italic;">
If you provide your email address above, then by submitting<br/>
this form you agree that we may contact you by email<br/>
to follow up on your feedback.<br/>
</p:column>
</p:row>
<p:row>
<p:column>
<p:outputPanel style="text-align:right;">
<p:commandButton value="Send" type="button" onclick="PF('fabWidget').close();"/>
</p:outputPanel>
</p:column>
</p:row>
<p:row>
<p:column>
<p:spacer height="50"/>
</p:column>
</p:row>
</p:panelGrid>
</p:overlayPanel>