Screw the loose paneling to the cut off 2 x 4's.
Turn off the circuit to the existing can lights in the kitchen. Pull out the can light nearest your wall.
Drill a hole that will be covered by the new soffit.
Measure and cut supports to use in the new soffit. Drill 1/2” holes to run the non-metallic building electrical wire through (Image 1).
Nail the 2 x 4's to the old wall studs and, using them as a brace, attach the new 2 x 4's to build out the new soffit (Image 2).
Place blocking in between the studs where the light fixtures will hang (Image 3).
Measure out 2-1/2 feet from the wall for the first fixture, and 5-1/2 feet from the wall for the other and then drill holes to bring the non-metallic building electrical wire through.
Set the pancake boxes for the fixtures (Image 1).
Pull the non-metallic building electrical wire into the boxes (Image 2).
Electrical codes vary from city to city and county to county. Before you begin any rewiring, it is a good idea to check with your local building inspectors.
Once the frame for the new soffit is up and the electrical boxes for the lights are installed complete with wiring, you need to put up new drywall. Attach the drywall to the new frame with drywall screws.
Note: A new soffit was a better solution instead of trying to patch and repair the ceiling where the wall was removed.
Apply a thick layer of joint compound to the seam, making sure to fill the space between.
Press the drywall tape into the mud, and smooth it out. Go along and fill in each screw head.
Rip a 12 foot 1 x 10 foot fascia board to 8-3/8 inches wide on the table saw. Measure off the same distances as your electrical boxes and cut out holes to accommodate it and install it under the soffit.
Once the fascia board is in place, secure it with 2-1/2 inch finishing nails.
Once the drywall mud is dry, apply a second layer of mud over the tape. When the second layer has dried, smooth everything out by lightly sanding over the mud.
Drywall is a very versatile material. It comes in 5/8 thickness all the way down to 1/4”. It can be bent, shaped or drilled and the best part about it is that any do-it-yourselfer can do this job.