1. Define a kanban view for the tasks:

<record id="kanban_tasks" model="ir.ui.view">
    <field name="name">project.task.kanban</field>
    <field name="model">project.task</field>
    <field name="sequence">20</field>
    <field name="arch" type="xml">
        <kanban default_group_by="stage_id">
            <field name="stage_id" />
            <field name="name" />
            <templates>
                <t t-name="kanban-box">
                    <div class="oe_kanban_card oe_kanban_global_click">
                        <field name="name" />
                    </div>
                </t>
            </templates>
        </kanban>
    </field>
</record>

2. Add a menu and an action using this view. This is left as an exercise for the reader.