In my lounge I have purchased a solid oak shelf to go above my wood burning stove. The shelf has come with this type of fitting.
The issue I have is that I don't know how to fasten these due to the makeup of the wall. The construction working from outside to inside is: Solid external wall, 3x2 timbers fastened to the masonry, plasterboard then screwed into these timbers with insulation between the timbers. The length of the fittings provided are longer than the depth of the 3x2 battens, meaning about 20mm of the screw will need to go past the battens into the masonry behind, but how do I drill into the masonry to accommodate the screw head without making the hole in the timber too large for the screw to grip onto?
The screws themselves are 3 inches/70mm long. The studs/battens to screw into are only 1.75 inches/45mm thick.
I'm a bit stuck and would appreciate advice.
Here is an image of the studs/battens:

