Melt 1 tablespoon butter in an oven-proof skillet over medium heat; stir in corn and tarragon and cook, stirring occasionally, until corn begins to brown, about 5 minutes.
Place skillet with corn in the preheated oven; roast, stirring every 5 minutes, until lightly browned but not dry, about 20 minutes.
Place bacon in a Dutch oven over medium-high heat; cook, turning occasionally, until evenly browned, about 10 minutes. Remove bacon slices; drain on paper towels. Pour off all but 1 tablespoon bacon fat.
Heat reserved bacon fat in Dutch oven over medium heat; stir in onion. Cook and stir until onion has softened and turned translucent, about 5 minutes. Reduce heat to medium-low, and continue to cook and stir until the onion is very tender and dark brown, about 15 minutes.
Pour chicken stock over caramelized onions; stir, scraping the bottom of the pot to dissolve any browned bits, and bring to a boil. Stir potatoes, parsley, garlic, celery, and paprika into onion mixture. Crumble bacon, reserving about 1/4 cup for garnish, and stir bacon into soup. Reduce heat to low; simmer until potatoes are tender, about 30 minutes.
Stir remaining 2 tablespoons butter and half-and-half into soup; season with salt and pepper. Sprinkle reserved bacon and Cheddar cheese over soup to serve.
