Moments after the recipe site SimmerHearth.com assured Rachel Amdahl, 29, that it valued her privacy, the site reportedly accompanied her to eleven other websites, took detailed notes on everything she looked at, and mentioned her to 847 partners, several of whom it described as “close.”

The assurance appeared in a warm serif font over a photograph of bread, above two buttons: “Accept All,” rendered in a proud green, and “More Options,” rendered in the gray of a November sky.

More Options, Ms. Amdahl reports, contained 847 individual toggles, each preset to On, followed by a second tab titled Legitimate Interest, where the same 847 partners waited, toggled On again, in case she got past the first ones.

“I clicked Reject All,” Ms. Amdahl said. “A new banner appeared. It said, ‘We noticed you rejected all. Are you sure?’ The buttons were ‘I’ve Changed My Mind’ and ‘Ask Me Again in One Hour.’ There was no third button. I checked behind the bread.”

SimmerHearth is operated by the ad-technology firm Panoptico, whose chief trust officer, Bram Cardiff, defended the design. “Privacy is sacred to us. It is the single most valuable thing our users possess,” he said. “We know precisely how valuable. We’ve priced it. It’s 43 cents.” Mr. Cardiff added that the company honors every consent choice by recording it, storing it indefinitely, and sharing it with its partners “so that they, too, can honor it.”

An industry group, the Coalition for Meaningful Consent, defended the banner as a triumph of user choice. “Eight hundred forty-seven toggles is eight hundred forty-seven opportunities to be heard,” said its director, reached at the group’s annual conference, which is titled Trust and held each year in a jurisdiction without a privacy law.

Ms. Amdahl ultimately consented 51 minutes after arriving, at which point the site displayed the recipe, which had been moved behind a $4.99-a-month paywall. She subscribed. The site thanked her warmly, and 847 partners were notified of the good news.