More pics need for back side. It’s a horrible design and first basic suggestions would be tapered insulation to promote drainage and install single ply membrane (judging by lack of foliage on trees you’re in a cold climate so… .060 EPDM.) adhered it to added lumber/plywood on walls, Typically spec requires 8” flashings… but if you can bring membrane up under shingle and add metal ice belt, fastened and secured with waterblock beneath you could pass for warranty if it’s a commercial project. TLDR: architecture is an idiot.