The beam attached to the house could be a 2" that is plenty for the joists to either sit on or using hangers be attached to.
You say your using a 4" beam why ?
Bearer attached to the block wall, joists either sitting on it or with joist hangers up to it, spanning out to the next bearer which would be supported with 4"x4" posts concreted into the ground at 8' centers over whatever the span your building it .
Using a 2x10" x (however long you need) drill into the 1/4" mortar gaps with a 1/2" masonry bit and using 1/2" concrete anchor bolts
bolt the beam to the blocks.
Using the same 2x10" x (however long you need) drill 1/2" holes through this board place it up against the wall at the desired location, mark to holes on the wall. Drill through the wall and into the basement area with a 1/2" masonry bit. Using another 2x10" on the inside (marked and drilled with holes to match the exterior beam) and using 12" galvanized coach bolts bolt the two beams on either side of the blocks (one in and one out) sandwiching the block wall.
You could use pieces of 2 x 10" 24" long as the support blocks on the inside of the basement instead of a long length of lumber.