In a large pot add the olive oil to heat, add the onion, <g class="gr_ gr_78 gr-alert gr_gramm gr_disable_anim_appear Punctuation only-ins replaceWithoutSep gr-progress" id="78" data-gr-id="78">garlic</g> and squash. Leave on <g class="gr_ gr_62 gr-alert gr_spell gr_disable_anim_appear ContextualSpelling ins-del multiReplace" id="62" data-gr-id="62">medium high</g> heat until vegetables are browned.
Add the salt, oregano, and dried chili and give it a few turns until the oregano releases its odor, about three minutes.
Add the tomatoes.
Add the water or vegetable stock, remove the chili if you do not want to chop the soup a lot, cover and leave for 10-15 minutes until the vegetables are super soft.
Put it in the blender and blend until the soup is creamy. Return to the pot and make the sandwiches.
In a small skillet, add 1 teaspoon of oil and two slices of bread. Divide the cheese into each and cover with another slice of bread. Turn the pan over medium heat until the bread is browned and the cheese is melted. Turn and let it brown on the other side. Cut each sandwich into cubes.
Serve the soup in a bowl and drizzle a bit of olive oil, chopped basil and a few squares of grilled cheese.