To clean leeks: chop off ends and peel any rough layers from the outside. Slice and place in a large bowl. Fill the bowl with water and using your hands, continually toss leeks to loosen any dirt. Do this for about 5 minutes. Remove and place on a towel to dry.
Toss chopped chicken with 1 teaspoon of salt and pepper, paprika and nutmeg. Heat a large stock pot over medium-high heat and add 2 tablespoons olive oil. Add in chicken in one layer and cook until golden brown on each side – about 2-3 minutes per side. Once finished, remove with a large slotted spoon and place in a bowl. Reduce heat to low, adding remaining olive oil and toss in leeks with remaining salt and pepper. Stir to coat, then let cook for 5-6 minutes until soft.
Add in garlic and stir, cooking for 1 minute, then toss in carrots, squash, sweet potatoes, torn kale and cooked chicken. Add chicken stock and bring to a boil. Once boiling, reduce to a simmer and cover, cooking for 20-30 minutes, until potatoes and squash are soft but nut mushy.
While the soup is cooking, heat butter in a small saucepan over medium heat, whisking constantly. Stir until brown bits appear on the bottom and then immediately remove from heat, stirring for another 30 seconds or so.
Before serving soup, add in grated parmesan cheese and stir well. It is your choice if you’d like to stir in all of the brown butter at once or drop a few teaspoons in each bowl as it is served. I like to stir it in all at once – such great flavor. Top with a few extra shavings of parmesan.