One challenging project involved creating a responsive design for a website with complex layouts and varying content sizes. I overcame the difficulties by using CSS Grid and Flexbox to create flexible, adaptive layouts. I also utilized media queries to ensure the design was optimized for different screen sizes. Additionally, I implemented CSS variables to manage and update styles efficiently across the site.

To ensure cross-browser compatibility, I start by testing my CSS in multiple browsers during development. I use tools like BrowserStack to simulate different environments. I also leverage CSS resets and normalize.css to reduce inconsistencies. For more complex issues, I use feature detection with Modernizr and provide fallbacks or polyfills where necessary.

To optimize CSS performance, I minimize the use of expensive CSS properties like `box-shadow` and `border-radius` on large elements. I also combine and minify CSS files to reduce the number of HTTP requests. Additionally, I use CSS animations and transitions instead of JavaScript where possible, as they are more efficient. Finally, I ensure that unused CSS is removed to keep the file size minimal.

To handle CSS specificity issues, I follow a consistent naming convention, such as BEM (Block, Element, Modifier), to keep styles modular and avoid conflicts. I also use utility-first CSS frameworks like Tailwind CSS, which reduces the need for complex selectors. When specificity issues arise, I use the `!important` rule sparingly and refactor the CSS to reduce complexity.

My approach to writing maintainable and scalable CSS involves using a modular architecture, such as Atomic CSS or SMACSS (Scalable and Modular Architecture for CSS). I also document my CSS with comments to explain the purpose of each section. Additionally, I use preprocessors like SASS to nest styles and create reusable mixins. This helps in organizing the codebase and making it easier to update and extend in the future.