DIAGNOSIS This isn't a filter problem—it's a thermal mass problem. The plastic pitcher and the large volume of water simply take a long time to chill down from room temperature, especially if you're refilling it with warm tap water.
FIX You need to pre-chill the water. 1) Always use the coldest tap water available to fill the reservoir. 2) After filtering, if you need cold water fast, pour the filtered water into a sealed bottle or container and lay it on its side in the freezer for 20-30 minutes. 3) For generally colder water, keep a dedicated space for the pitcher at the back of the fridge, near the cooling vent, and avoid opening the fridge door frequently.
IF THAT DIDN'T WORK Consider if your fridge is actually cooling properly. Use a thermometer to check that your fridge interior is at or below 40°F (4°C). If it's warmer, the pitcher water won't get cold.
HEADS UP Don't put the Brita pitcher in the freezer to speed up cooling. The plastic can become brittle and crack, and if the water inside freezes, it will expand and likely split the pitcher.