A boundary works where a ban does not
Shutting the kitchen door solves cooking hour but teaches your dog nothing, and most homes cannot keep doors closed all day anyway — people, shopping, and other rooms all flow through the kitchen. What he can learn, reliably, is a line: on this side, during cooking, is where dogs are; the mat at the doorway is his post, and good things arrive there. Dogs understand well-paid geography far better than they understand rooms being sometimes forbidden and sometimes not. Your whole training job is to make that line obvious, make the allowed side rewarding, and make the rule identical at breakfast, at dinner prep, and when guests are cooking.
Choose the line and mark it physically
Pick the boundary he can actually see: the edge of the kitchen flooring, the end of a run of cabinets, a change from tile to wood. Put his mat just on the allowed side of that line, positioned so he can watch the cooking without being underfoot — dogs settle far better when they can see the activity they are excluded from. Begin training outside cooking times: lead him to the mat, ask for the settle, reward, release. Then add you standing at the counter doing nothing interesting, then chopping something plain. He should learn the mat and the line as a calm picture before a single pan heats up.
Build through real cooking, in the right order
Progress to genuine cooking in easy stages — a kettle and toast before a full roast with trays moving to and from the oven. During these sessions, one person cooks while, at first, another can be in charge of paying the settle: treats landing on the mat at lengthening intervals, always delivered on his side of the boundary, never tossed from the counter across the line. If he crosses, there is no drama: walk him back to the mat, re-settle, and make the next stretch shorter or the cooking simpler. The dangerous moments to plan around are specific — hot pans crossing the room, the oven door opening, food being carried to the table — and on complicated cooking days, a stair gate across the doorway is honest management while training continues on simpler meals.
Remove the payoffs that live inside the line
Boundary training fails quietly through scavenging. A kitchen floor during cooking rains crumbs, and a dog who once found a dropped piece of chicken under the counter has a standing reason to patrol inside the line. Wipe the floor before you start, bin scraps immediately rather than leaving them on the side, and position bins so he cannot raid them from his mat. And the household rule with no exceptions: nobody feeds him from the counter, the hob, or a plate, ever, because food arriving from inside the kitchen teaches him the kitchen is where his meals originate and the mat is merely where he waits for them.
One household, one line
This rule lives or dies on consistency between people. A teenager wandering through with toast, dropping both crumbs and the boundary, or a partner who calls him in to help with a dropped spoonful, will undo the careful version in a weekend. Write the arrangement down for everyone: where the line is, where the mat lives, who pays the settle during busy cooking, and when the gate goes up instead. Relatives you select gain entry to that profile when you open it to them, with Family Sharing on KinsLe.