Heat olive oil in a large Dutch oven over medium-high heat until shimmering. Working in batches to avoid crowding, brown beef cubes on all sides for 3-4 minutes per batch, developing a caramelized crust. Transfer browned meat to a plate and set aside—this Maillard reaction creates the foundation for deep, complex flavor throughout the stew.
Reduce heat to medium and add diced onion to the pot, scraping up browned bits with a wooden spoon. Sauté for 3-4 minutes until translucent, then add minced garlic and cook for 1 minute more until fragrant. Stir in tomato paste and cook for 2 minutes, allowing it to caramelize slightly and deepen in color.
Pour in beef broth, using a wooden spoon to deglaze the bottom completely. Return the browned beef to the pot along with thyme, rosemary, and bay leaves, stirring well to combine this best beef stew hearty base. Bring to a gentle simmer over medium-high heat, then reduce to medium-low and cover partially with the lid.
Simmer for 45 minutes, then add carrot rounds and potato cubes along with sliced mushrooms. Season with salt and pepper, stirring gently to incorporate vegetables into the cozy fall stew. Continue simmering for 25-30 minutes more until vegetables are fork-tender and the sauce has reduced slightly and thickened naturally.
In a small bowl, whisk cornstarch with cold water to create a slurry. Stir this into the stew and simmer for 2-3 minutes until the broth achieves a glossy, coat-the-spoon consistency. Taste and adjust seasoning—the sauce should feel luxurious and cling beautifully to each ingredient. Remove bay leaves before serving your elegant fall dinner creation.