Wash and dry all vegetables. Cut eggplant into 3/4-inch cubes, dice zucchini, yellow squash, bell peppers, and onion into similarly sized pieces. Mince garlic and chop fresh basil.

Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add diced eggplant and cook for 6-8 minutes, stirring occasionally, until softened and lightly golden. Transfer to a plate.

Add another tablespoon of olive oil to the skillet. Add diced zucchini and yellow squash. Cook for 4-5 minutes until slightly softened and lightly colored. Transfer to the plate with the eggplant.

Reduce heat to medium and add the remaining tablespoon of olive oil. Add onion and bell peppers, cooking for 5-6 minutes until softened. Stir in minced garlic and tomato paste, cooking for another minute until fragrant.

Return eggplant, zucchini, and yellow squash to the skillet. Add canned diced tomatoes with juices, dried thyme, salt, black pepper, and optional red pepper flakes. Stir gently and simmer uncovered over medium-low heat for 12-15 minutes until vegetables are tender and sauce thickens slightly. Add a splash of water if needed. Adjust seasoning and keep warm.

When ratatouille is nearly finished, combine vegetable broth and whole milk in a medium saucepan. Bring to a gentle simmer over medium heat. Slowly whisk in quick-cooking polenta. Reduce heat to low and cook according to package directions, approximately 5-8 minutes, stirring frequently until smooth and creamy.

Remove polenta from heat. Stir in crumbled goat cheese, unsalted butter, salt, and black pepper until completely melted and incorporated. If polenta is too thick, add a little warm milk, vegetable broth, or water until it reaches a soft, creamy consistency.

Spoon creamy goat cheese polenta into four shallow serving bowls. Top each portion with warm homemade ratatouille. Garnish with freshly chopped basil and serve immediately.