Melt the 2 tablespoons unsalted butter with the 1 tablespoon olive oil in a Dutch oven over medium heat. Add the 1 tablespoon all-purpose flour and whisk until no dry flour remains. Cook for 1–2 minutes, stirring frequently, until the mixture smells slightly nutty and loses its raw-flour aroma.
Add the small diced yellow onion and diced celery stalk. Cook for 5–6 minutes, stirring occasionally, until softened and translucent. Add the minced garlic clove and cook for 30 seconds, stirring constantly.
Gradually add the 4 cups low-sodium vegetable broth, stirring well to incorporate it into the flour mixture. Add the diced potatoes, 1 bay leaf, ½ teaspoon kosher salt, ¼ teaspoon black pepper, ¼ teaspoon sweet paprika, and ½ teaspoon dried thyme.
Increase the heat and bring the chowder to a boil. Reduce the heat to medium-low, cover, and simmer for 12–15 minutes, or until you can easily pierce the potatoes with a fork.
Whisk the 1 tablespoon cornstarch and 2 tablespoons cold water together in a small bowl until completely smooth. Slowly pour the slurry into the chowder while stirring.
Simmer uncovered for 2–3 minutes, stirring occasionally, until the broth begins to thicken.
Reduce the heat to low. Stir in the ¾ cup half-and-half, 12 ounces hot-smoked salmon, 2 tablespoons chopped fresh dill, and 2 tablespoons capers, if using. Simmer gently, uncovered, for 5 minutes, or until the salmon is warmed through. Do not let the chowder boil.The hot-smoked salmon will release flavorful oils as it warms, creating visible droplets on the surface. This is normal and gives the chowder its rich salmon flavor. Remove the pot from the heat. Stir in the 2 teaspoons freshly squeezed lemon juice. Remove and discard the bay leaf and fresh thyme sprigs, if used.
Taste and adjust the salt and pepper as needed. Ladle the chowder into bowls and serve warm.