Melt the butter over medium heat in a 4- or 5-quart Dutch oven or other heavy-bottomed pot. Add the chopped onion and cook for 2-3 minutes, stirring occasionally until softened and translucent. Do not let the onion brown.

Stir in the garlic, ½ teaspoon salt, smoked paprika (if using), and cayenne. Cook for 1 minute, until fragrant.

Sprinkle the flour over the onion mixture. Cook, stirring constantly, for about 1 minute, until the flour forms a paste-like coating on the onions.

Gradually whisk in ½ cup chicken broth until smooth and fully incorporated. Add the remaining 2 ½ cups broth, drained and rinsed roasted red peppers, and thyme sprigs.

Bring to a boil, then reduce the heat to medium-low. Cover and simmer for approximately 30 minutes, or until the red peppers are very soft and ready to blend.

Remove and discard the thyme sprigs. Using an immersion blender, purée the soup until smooth.

Remove the pot from the heat, and stir in the grated Gouda in batches, stirring continuously until each addition has melted before adding more. Scrape the bottom of the pot as you stir to prevent the cheese from sticking.

Briefly use the immersion blender to fully incorporate the Gouda and create a smooth consistency.