Peel and mince shallot. Core Roma tomato and cut into 1/4" rounds. Halve lime and juice. Halve avocado and remove pit by carefully tapping pit with the blade of your knife so it sticks. Gently twist knife to release pit. Scoop out the flesh with a spoon and into a small bowl. Add 1 tsp. lime juice, 1/4 tsp. salt, and a pinch of pepper to bowl with avocado. Mash with a potato masher or spoon to form a chunky puree. In another small bowl, combine half the sour cream and 1 tsp. lime juice.

Place a cheddar slice on each slice of bread. Top two bread slices with mashed avocado and Roma tomato rounds. Top with other slice of bread.

Heat 1 tsp. olive oil in a medium pot over medium heat. Add shallot to hot pot and cook, stirring often, 2 minutes, or until shallots become translucent. Add vegetable base, crushed tomatoes, and 1 cup water to pot. Bring to a simmer and cook 8-10 minutes, or until slightly thickened. Season with 1/2 tsp. salt and 1/4 tsp. pepper. Remove from burner and whisk in remaining sour cream. Cover and keep warm.

While soup simmers, heat 2 tsp. olive oil in a large non-stick pan over medium-high heat. Add sandwiches to hot pan and cook 2-3 minutes per side, or until bread turns golden brown. Add an additional 1 tsp. olive oil to pan if needed. Transfer sandwiches to prepared baking sheet.

Top each sandwich with shredded Asiago and bake 5-6 minutes, or until Asiago is melted. Transfer sandwiches to cutting board and let rest at least 5 minutes before halving on an angle.

Serve sandwiches on a plate with tomato soup on side. Garnish soup with a dollop of lime crema.