Module page
Place blocks with a referenced entity and selected view mode.
Alternatives
Content block type
This could be built instead as a content block type with an entity reference field and view mode selector using Field View Mode module.
That would give you more flexibility, like adding more fields to the parent block, or configuring different display modes for the wrapper.
Entity Blocks says it can be fieldable, is it?
View
Create a view with a contextual filter for the entity ID.
Configure the view to show the custom display mode.
Place as a block.
Core module
no
Stability
Stable