Create the Corn Stock: In a saucepan, combine the corn kernels, milk, and 2 crushed garlic cloves. Scrape the milk and pulp from the reserved cobs into the pan with the back of a knife, then add the cobs.

Bring to a boil, then immediately remove from heat and let it steep to infuse the flavors.

Sauté the Aromatics: In a large Dutch oven, heat the butter and 1 tbsp (15 ml) of olive oil over medium-low heat.

Add the sliced leeks, cover, and cook for 15 minutes, stirring occasionally, until very soft.

Stir in the 3 minced garlic cloves and smoked paprika and cook for 30 seconds until fragrant.

Pour in the sherry, cook for another 30 seconds, then add 4 cups (960 ml) of water and remove the pot from the heat for now.

Brown the Vegetables: In a separate skillet, heat 1 tbsp (15 ml) of olive oil over medium-high heat.

Add the diced sweet potatoes and sauté for 8 minutes until nicely browned, then transfer them to the Dutch oven.

In the same skillet, add the final 1 tbsp (15 ml) of olive oil, add the green beans, and sauté for 3 minutes.

Set the green beans aside on a plate.

Simmer the Chowder: Bring the mixture in the Dutch oven to a boil.

Reduce the heat to medium-low and simmer for 5 minutes to soften the sweet potatoes.

Stir in the sautéed green beans and cook for 4 more minutes until tender-crisp.

Finish and Serve: Strain the steeped corn-milk mixture through a fine-mesh sieve into the chowder, discarding the cobs and garlic.

Stir in 1 tbsp (15 ml) of the chopped cilantro.

Season to taste with salt and pepper.

Serve hot, garnished with the remaining cilantro and fresh lime wedges on the side.