Wash and dry all produce. Preheat oven to 425 degrees. Put 1 TBSP butter in a small microwave-safe bowl and let sit at room temperature. Cut potatoes into 1/2-inch cubes. Core and seed poblano, then cut into 1/2-inch pieces. Halve, peel, and finely chop onion. Trim, then thinly slice scallions, separating greens and whites. Mince or grate garlic.

Heat a large drizzle of oil in a large pot over medium-high heat. Add poblano, onion, scallion whites, and half the garlic. Cook, tossing, until very soft, about 5 minutes. Season with salt, pepper, and half the paprika. Add flour and stir until pasty, about 1 minute. Slowly whisk in milk, a little at a time, until fully incorporated.

Add potatoes, 11/2 cups water, and stock concentrate to pot. Bring to a boil, then lower heat and reduce to a simmer. Cook, stirring occasionally, until potatoes are easily pierced by a knife, 12-15 minutes.

While soup simmers, add remaining garlic to butter in bowl. Warm in microwave until soft but not melted, about 10 seconds. Season with salt and pepper, then stir to combine. Halve demi-baguette lengthwise and spread garlic butter evenly onto cut sides. Season with salt and pepper. Place on a baking sheet cut-side up and toast until golden, about 5 minutes.

Once soup is done simmering, drain corn, then stir into pot. Stir in remaining paprika. Simmer 3-5 minutes more. Turn off heat and stir in cheddar. (TIP: If soup seems thick, stir in 1/4-1/2 cup more water.) Season with plenty of salt and pepper.

Divide soup between bowls and garnish with scallion greens. Cut toasts into triangles and serve on the side.