Need ideas on how to secure these overhangs on a lean-to roof.

[PaulsWife]

Building a house with a lean-to style roof. Hubby and I need ideas on how to secure the overhangs to the beams. Attached are photos of what it will look like. 

[MountainDon]

The normal method is to run the rafters from the upper wall top down to and over the lower wall. Spacing could be 12 to 24 inches depending on span distances live and dead loads, etc. Depending on the span  that may be accomplished with dimensional lumber, or some type of manufactured truss or rafter. An intermediate beam, parallel to the high and low walls may be used and would need to be engineered.

What are the bldg dimensions? Location or snow load if known?

Those little stubs as illustrated are not the best design.

A roof truss supplier would likely be able to assist in choices for the design. They would need dimensions, location, snow load etc.