Place a large baking sheet in oven. Preheat oven to 450°.
To prepare veggies, combine the cornmeal and cheese in a small bowl, stirring well. Place potato and carrots in a large bowl. Drizzle vegetables with 2 tablespoons oil. Sprinkle vegetables with 1/4 teaspoon salt and 1/4 teaspoon pepper; toss. Sprinkle the cornmeal mixture over vegetables; toss. Arrange vegetables in a single layer on preheated baking sheet; bake at 450° for 15 minutes. Turn vegetables over; bake an additional 8 minutes or until golden and tender.
To prepare steaks, heat a medium saucepan over medium-high heat. Add wine and the next 4 ingredients (through rosemary) to pan, and bring to a boil. Cook until liquid almost evaporates (about 8 minutes). Add broth; bring to a boil. Cook until reduced to about 1/2 cup (about 13 minutes). Remove from heat; strain mixture through a sieve over a bowl. Discard solids.
Heat a cast-iron skillet over medium-high heat. Add 1 tablespoon oil to pan; swirl to coat. Sprinkle both sides of steaks evenly with 1/4 teaspoon salt and 1/4 teaspoon black pepper. Add steaks to pan; sauté for 3 minutes on each side or until desired degree of doneness. Let steaks stand 5 minutes.
Heat pan to high heat. Add reduced broth mixture to pan; stir in mustard and remaining 1/8 teaspoon salt. Remove from heat. Add butter to pan, 1 piece at a time, stirring with a whisk until each addition is incorporated. Place 1 steak on each of 4 plates; drizzle each serving with about 1 tablespoon sauce. Sprinkle each steak with 1/2 teaspoon thyme leaves, if desired. Divide the vegetable fries evenly among servings.