I have problem skin on my feet that started with puberty. I've had to use a file every week of my life for decades to keep on top of it or I get a thick layer of hard skin that cracks like yours, OP.
I use a Microplane but have found over the years that using a cheese-grater type file or one of those hard skin shaver type tools encourages the skin to thicken up quicker.
My method that has enabled me to go from weekly to monthly filing starts with a microplane to get rid of the worst (always on DRY skin). Then I'll follow with a sandpaper type of file (either a battery rotational type or the Margaret Dabbs foot file). Then, if there's still any roughness, I fine it off with a glass file. The etched ones like Spa-rific do the best job.
I use a foot cream almost every night with a pair of socks on top. Margaret Dabbs Foot Hygiene is good but any thick cream will do.
One of the PP suggested glycolic acid followed by Vaseline which is a great suggestion.
Years ago I got hold of a large tub of 20% salicylic acid ointment from the pharmacist. This stuff was AMAZING. Thick and gloopy, needed old socks on top but did the job better than anything else I've ever tried. If someone knows where I can get some, please can you post? Mine must have been a pharmacy formulation as the pharmacist (retired years ago) had used it to make up other preparations.
My DP had cracks like that. I filed off what I could (dry skin), then applied the SA ointment. I kept doing this for days. I bought silicone heel socks to help stop the skin drying out. He'd had Athlete's Foot in between his toes so I tackled that with an anti-fungal foot powder but used the cream version on his heels. It took a few weeks but it worked.
A fungal infection can cause or worsen cracked heels so try an anti-fungal cream. The Margaret Dabbs Hygiene cream is good but it won't get rid of an established fungal infection.
A product I've used for years for all kinds of hard skin, including corns, is J. Pickles cream. I think it's been discontinued now which is a big shame as it's a very effective product. I get very hard skin growing up around the sides of my toenails but a dab of this stuff on the area for 5 nights and the skin is baby soft again.
The PP who suggested changing to Birkenstocks is spot on, too.