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Step-by-step build — 7 steps. Also available as a print sheet.
Each leg set is a tall back leg and a short front leg joined by a 2x4 counter support up top and a 2x2 bottom-shelf rail lower down. Build all three identical — two screws into the 2x4s, one per 2x2 joint.
Pre-drill every screw in this build: 2x2 stock splits near its ends without a pilot hole, and nearly every joint here lands near an end.
Connect the three leg sets with a front rail and a back rail, two screws per joint, the middle leg set centered. Stand it on flat ground and check for rock before the final screws — a three-legged-table wobble is much easier to fix now than after the counter's on.
Add the remaining 2x4 supports — the rest of the counter bearers and the backsplash rail across the tall legs. Everything the pickets land on should now be in place.
Lay picket boards across the bottom rails, notching the front board around the legs with the jigsaw. Screw down with even gaps between boards — the gaps are the drainage plan, and a mud kitchen without drainage is a mosquito farm.
Screw the counter pickets down with even gaps. Then trace your actual wash bin upside down where the sink goes, draw a cut line about 1/2" INSIDE the traced rim, drill a 1/2" starter hole, and jigsaw the opening. Drop the bin in — the rim hangs on the counter, and lifts out for dumping.
Trace the real bin, not a measurement of it. Bins taper and their rims aren't square, and a hole cut to the catalog dimension is how bins fall through counters.
Screw the backsplash board across the tall legs, flush to their tops. Attach the shelf board to the bottom edge of the backsplash, then fit the three 45° brackets under it — the brackets carry the real load when the shelf gets leaned on, which it will.
Cut those brackets from the end of a long 2x2, clamped to the saw. Seven-inch pieces and fingers do not share a saw fence.
If the chef wants burners, cut rings from picket scraps — drill a 1/2" hole and connect the circle with the jigsaw — and screw them to the counter.
Then the most important step on a kids' build: sand everything, round every corner, and run your bare palm over every surface a kid will touch. Finish with a kid-safe penetrating oil or let the cedar silver. Stock with pots, spoons, and a strict no-mud-in-the-house treaty.