Rinse the split peas under cold water and set aside. Clean the leek by slicing it lengthwise, rinsing between layers to remove any dirt, then slice into half-moons. Cut broccoli florets into bite-sized pieces (about 1-2 inches) so they cook evenly and are easy for kids to eat. Measure out all remaining ingredients so everything is ready when you need it. Heat the butter in a large pot over medium heat until it foams, then add the sliced leek and cook for 5 minutes, stirring occasionally, until it softens and becomes slightly translucent—this builds a sweet, mild flavor base that kids will enjoy.

Add the rinsed split peas to the softened leeks, stirring to coat them with the butter. Pour in the chicken broth and add the salt, garlic powder, and pepper—garlic powder gives a gentle, familiar flavor that appeals to kids rather than raw garlic's sharpness. Bring the mixture to a boil over medium-high heat, then reduce the heat to medium-low, place a lid partially on the pot (leaving a small gap for steam to escape), and simmer for 30 minutes. This allows the split peas to break down and thicken the soup naturally while developing deep flavor.

Add the broccoli florets from Step 1 to the simmering broth and split pea mixture. Cover the pot and continue cooking on low heat for 10 minutes, until the broccoli is very tender and easy to mash—this ensures it breaks down into a smooth, creamy texture that kids prefer and makes blending easier.

Remove the pot from heat and uncover it. Pour in the whole milk to add creaminess without making the soup taste overly rich or heavy—I find this balance is exactly what kids want. Using an immersion blender, blend the soup until it reaches your desired consistency; I prefer it smooth but with just a hint of texture so kids can still identify the vegetables. If you don't have an immersion blender, carefully transfer the soup in batches to a regular blender and blend until smooth, then return it to the pot.

Stir in the grated sharp cheddar cheese until it's completely melted and the soup is smooth and creamy. The residual heat will melt the cheese perfectly without needing additional cooking. Taste and adjust seasoning if needed, then ladle into bowls and serve while hot.