To make soup, heat olive oil in a large saucepan over medium-high heat. Add onion, garlic, sage, and thyme. Reduce heat to medium-low, and cook, stirring occasionally, until mixture is soft and fragrant, about 3 minutes.
Stir in tomato paste and cook while stirring constantly until tomato paste darkens, about 1 1/2 to 2 minutes. Add canned tomatoes and their juices and simmer, stirring occasionally, until slightly thickened and reduced, about 7 minutes. Remove thyme sprigs and discard.
Transfer mixture to a food processor and pulse to combine. Add chicken broth, almond milk, and yogurt, and process until completely smooth.
Pour soup back into a clean pot and cook over medium heat until warm, about 5 minutes. Stir in sea salt. Serve with a dollop of yogurt and some chopped fresh basil, if using.
To make grilled cheese bites, mix mustard and mayonnaise together in a small bowl and spread on 2 bread slices. Top with 2 slices cheese and 3 slices deli meat (if using), then cover with a final cheese slice. Place remaining bread slices on top.
Heat olive oil in a medium nonstick skillet over medium heat. Add sandwiches and grill until browned, about 2 minutes. Flip over and brown on other side, 1 to 1 1/2 minutes longer (check often as second side usually browns more quickly than the first). Transfer sandwiches to a cutting board and let cool for 2 minutes before removing crusts with a serrated knife. Slice each sandwich lengthwise into 4 even fingers. Serve with soup.