Heat the oil in a sauce pot over medium heat. Add the onions, garlic and carrots and sauté until veggies are soft, about 5 minutes.: You will notice a gentle shimmer on the surface of the olive oil when it is ready, and the pan should be warm but not smoking. Heating the oil properly ensures even cooking of aromatics and prevents sticking. If the oil smokes, reduce the heat immediately and let the pan cool a touch, because overheated oil will turn bitter and ruin the dish.
Add the tomatoes and salt and simmer for 20 minutes. Remove from the heat and puree until smooth using an immersion blender, or carefully transfer to a regular blender and puree.: As you add the diced onion , minced garlic , and diced carrot , listen for a soft sizzle and inhale the sweet, savory perfume that builds. Stir frequently so pieces brown evenly and become translucent, which releases natural sugars that create depth. Watch for the garlic to brown too fast; if it does, it will taste harsh, so lower the heat and continue to cook gently until all vegetables are tender.
Cook the gnocchi according to package directions.: When you pour in the diced tomatoes and sprinkle the kosher salt , the mixture will steam and bubble steadily as it reduces. This simmer concentrates the tomato flavor and softens acidity, yielding a rounder sauce. Keep the heat at a steady simmer so the sauce reduces without rapid splattering; if it boils too hard, the flavors will not develop evenly and the texture may become grainy.
Drain the gnocchi, add to the sauce and simmer for 2 minutes.: After removing the pot from heat, the aroma will deepen as the steam subsides. Pureeing transforms the chunky mixture into a silky, cohesive sauce that clings to the gnocchi . If using a regular blender, blend in batches and hold the lid with a towel to prevent hot splashes; failure to vent can cause dangerous eruptions. A too coarse texture will not coat the gnocchi as luxuriously, while overblending very long can warm the sauce excessively.
Top the gnocchi with basil, parmesan cheese and mozzarella cheese balls.: As you drop the prepackaged gnocchi into gently boiling water, you will hear a soft bubbling and see the pieces tumble. They are usually done when they float to the surface, which signals they are cooked through and pillowy. Avoid leaving them in the water too long, because prolonged cooking makes them swell and lose structure, turning pleasant pillows into mushy blobs.
Drain the gnocchi, add to the sauce and simmer for 2 minutes.: After you drain the gnocchi , toss them gently into the warm sauce and let them simmer together; you will see the sauce cling and small bubbles form around the edges. This brief simmer allows the starch on the gnocchi to marry with the sauce, integrating flavor and creating a cohesive coating. Stir gently to avoid breaking the pieces, and do not over simmer, because they can absorb too much liquid and become heavy.
Top the gnocchi with basil, parmesan cheese and mozzarella cheese balls.: Finishing with thinly sliced basil , grated parmesan , and soft mozzarella balls adds aromatic freshness and creamy contrast. The heat will slightly wilt the herb and soften the cheese without turning it rubbery, creating pockets of creaminess. If you add the cheese too early, it will fully melt and lose the pleasant textural contrast that makes the dish special.