Thaw burgers in refrigerator overnight.
Season liberally with burger rub on all sides.
Bring a large cast-iron pan to medium-high heat and add half of grapeseed oil.
Add 2 burgers to pan and cover with parchment paper, then smash with burger press or another cast-iron pan to about 1/2" thickness.
Cook burgers for about 2 minutes, until nicely seared.
Flip burgers, add 2 slices of Swiss cheese to each burger, add beef stock to the pan, and cover with lid; cook for about another 90 seconds to 2 minutes until cheese is fully melted and burger is cooked to desired doneness.
Remove burgers from pan, wipe clean, and repeat process with remaining 2 burgers, grapeseed oil, Swiss cheese, and beef stock.
Bring a separate large pan bring to medium heat.
Slather mayonnaise on one side of each slice of rye bread and toast in the pan until golden brown and crisped, about 90 seconds to 2 minutes on each side. Chef’s note: don’t overcrowd the pan; do it in two separate batches of 4 bread slices.