In a large stockpot, melt butter over medium heat. Add onions and carrots; sauté until onions are tender and translucent (about 5 minutes).: The smell of butter warming should be the first cue, with a gentle hiss as the diced onion and carrots hit the pot. You will notice the onion becoming glossy and soft, losing its raw bite, while the carrots begin to sweeten and release faint fragrant starchiness. This step builds the aromatic foundation, so resist the urge to rush the heat higher; too hot and the vegetables will brown instead of sweating. If you see browning, reduce the temperature and gently stir, scraping any fond from the pan to incorporate flavor rather than letting it burn.
Add garlic and thyme; continue to cook for 2 minutes.: A brief burst of minced garlic and the herbal scent of fresh thyme should perfume the pot within seconds. The garlic should soften and yield its aroma without taking on a bitter note; that delicate roasted garlic scent signals readiness. Use a wooden spoon to nudge the herbs among the vegetables so their oils bloom. Watch closely, because garlic can go from fragrant to scorched quickly; if the aroma turns acrid, add a splash of the chicken broth to cool the pan.
Stir in roasted red peppers, sundried tomatoes, tomato paste, fire-roasted tomatoes, chicken broth, all the seasonings, and sugar. Mix thoroughly.: As you add the roasted red peppers and sundried tomatoes , you'll see color deepen and texture diversify, with the tomato paste beginning to cling to the vegetables and toast slightly. The canned fire roasted diced tomatoes bring juices that sizzle and mingle, and the broth loosens everything into a cohesive base. Stirring is crucial here to dissolve the paste fully and disperse the seasonings evenly; pockets of concentrated paste will create sharp spots. If the mixture feels too acidic, the granulated sugar will begin to round that edge as it dissolves into the liquid.
Cover and simmer over medium-low heat for 15 minutes.: During the simmer, aromas should evolve from bright tomato tang to a deeper, richer tomato character with underlying roasted notes. Gentle bubbling at the edge of the pot indicates the right temperature, which allows flavors to marry without aggressive evaporation. This resting period also softens any remaining vegetable texture so the blend is seamless. A common mistake is boiling too hard, which can break down the gentle sweetness; lower the heat if you see rapid rolling bubbles and adjust the lid to maintain a slow simmer.
Carefully blend the soup using an immersion blender until creamy and smooth.: When you begin blending, expect a satisfying whirl and thickening of texture as chunks dissolve into a unified velvety body. The sound will shift from bubbling to a steady blending hum, and visually you will see the soup go from chunky to glossy and smooth. Keep the blender tip submerged to prevent splatter, and pause to scrape the sides if necessary so everything emulsifies evenly. If you have large unmixed pieces, pulse the blender instead of running continuously to avoid hot splashes. Overblending can incorporate too much air, making the soup foam; blend just until smooth.
Mix in heavy whipping cream and grated parmesan cheese; heat for an additional 3 minutes or until hot.: As the heavy whipping cream swirls into the hot base, the soup will visibly lighten and take on a luxurious sheen. The grated parmesan cheese should melt into a silky mouthfeel, adding savory umami and a slight nuttiness. Keep the heat gentle to coax the cheese into the soup without causing it to clump. If the soup separates or looks curdled, lower the heat and whisk vigorously; this usually smooths it back together. Avoid prolonged boiling after adding dairy to preserve creaminess.
Serve hot, topped with shredded parmesan cheese if you like.: The final presentation should steam gently, and the aroma of cheese and tomato should be inviting. Spoon the soup into bowls and finish with a sprinkle of shredded parmesan cheese for texture contrast and a salty lift. Listen for soft spoons clinking and notice the soup’s body on the tongue; it should be silky, slightly sweet, and warmly spiced. A mistake to avoid is letting the soup sit uncovered too long, which cools and thickens it; keep it ladled and covered until ready to serve.