That direction was filing formal charges, called a statement of objection, accusing Google of favoring its own comparison shopping service, called Google Shopping. In practical terms, the commission found that when a consumer used Google to search for shopping-related information, the site systematically displayed the company’s own comparison product at the top of the search results — “irrespective of whether it is the most relevant response to the query,” Ms. Vestager said in a commission-issued statement about the charges.

Google has 10 weeks to respond, she said, and has the right to call a hearing to present the company’s views.

In a blog post last week, Amit Singhal, senior vice president for Google Search, disputed the charges. “While Google may be the most used search engine, people can now find and access information in numerous different ways — and allegations of harm, for consumers and competitors, have proved to be wide of the mark,” he wrote.

Ms. Vestager may have a wider agenda. In addition to the formal complaint related to Google Shopping, Ms. Vestager said her office was still looking into accusations that Google had restricted its advertising partners from using rival platforms and that it scraped online content from competitors. She also announced a separate “in-depth investigation” into accusations of anticompetitive company practices regarding Google’s relationships with device manufacturers that rely on its Android operating system.

In a blog post last week, a Google executive said the company’s partnerships with manufacturers that relied on Android were voluntary and offered benefits to consumers and manufacturers.

Longtime observers of Ms. Vestager theorized that she had chosen to initially pursue a narrow case in which she had the most confidence, while keeping pressure on her adversary to settle by opening parallel lines of inquiry.

“It’s about power. Any deal she makes, it’s about how much power she has and how much power her adversary has,” says Martin Krasnik, the host of a late-night current affairs show on Danish national television who describes Ms. Vestager as the most impenetrable politician he has ever interviewed. “She’s totally unsentimental,” he said.